# Find The Distance Between Two Points (Real World Problems) Problems

7 questions

### #1 of 7:Medium

Find the distance between two points (real world problems)

<LineGraph data-props='{ "options": { "x_min": -10, "y_min": -10, "y_max": 10, "x_max": 10, "cell_size": 20, "x_interval": 1, "y_interval": 1 }, "points": [ { "id": 1, "x": 2, "y": 6, "show_point": false, "highlight_point": false, "highlight_point_color": "#377CF6", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "bank" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 2, "x": -3, "y": 7, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "theater" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 3, "x": 3, "y": -8, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "weight_lifter" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 4, "x": -7, "y": -3, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "books" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 5, "x": 8, "y": 7, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "police_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 6, "x": -8, "y": 6, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "mailbox" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } ], "line_segments": [], "legend_options": { "show_menu": true, "menu_position": "right", "menu_items": [ { "label": "Theater", "icon": { "name": "theater" } }, { "label": "Bank", "icon": { "name": "bank" } }, { "label": "Gym", "icon": { "name": "weight_lifter" } }, { "label": "Library", "icon": { "name": "books" } }, { "label": "Police station", "icon": { "name": "police_station" } }, { "label": "Post office", "icon": { "name": "mailbox" } } ] }}'></LineGraph ><p>You are currently at the post office, but you need to get to the bank.</p><ul><li>What are the coordinates for both the post office and the bank?</li><li>What is the distance between the post office and the bank?</li></ul> <p><highlight data-color="#666" data-style="italic">Each square represents `1` mile.</highlight></p>

### #2 of 7:Medium

Find the distance between two points (real world problems)

<LineGraph data-props='{ "options": { "x_min": -10, "y_min": -10, "y_max": 10, "x_max": 10, "cell_size": 20, "x_interval": 1, "y_interval": 1 }, "points": [ { "id": 1, "x": -8, "y": -8, "show_point": false, "highlight_point": false, "highlight_point_color": "#377CF6", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "airport" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 2, "x": 8, "y": -8, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "train_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 3, "x": -4, "y": -4, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "mailbox" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 4, "x": 8, "y": -4, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "city_hall" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 5, "x": -4, "y": 6, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "shopping_cart" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 6, "x": -8, "y": 6, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "hotel" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 7, "x": 2, "y": 6, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "books" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 8, "x": 6, "y": 6, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "gas_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }], "line_segments": [], "legend_options": { "show_menu": true, "menu_position": "right", "menu_items": [ { "label": "Library", "icon": { "name": "books" } }, { "label": "Post office", "icon": { "name": "mailbox" } } , { "label": "City hall", "icon": { "name": "city_hall" } }, { "label": "Shopping mall", "icon": { "name": "shopping_cart" } }, { "label": "Hotel", "icon": { "name": "hotel" } }, { "label": "Train station", "icon": { "name": "train_station" } } , { "label": "Airport", "icon": { "name": "airport" } }, { "label": "Gas station", "icon": { "name": "gas_station" } } ] }}'></LineGraph ><p>Kevin is currently at the city hall, but he needs to get to the post office.</p><ul><li>What are the coordinates for both the city hall and the post office?</li><li>What is the distance between the city hall and the post office? </li></ul><p><highlight data-color="#666" data-style="italic">Each square represents `1` kilometer.</highlight> </p>

### #3 of 7:Medium

Find the distance between two points (real world problems)

<LineGraph data-props='{ "options": { "x_min": -10, "y_min": -10, "y_max": 10, "x_max": 10, "cell_size": 20, "x_interval": 1, "y_interval": 1 , "x_skip_interval": 2, "y_skip_interval": 2 }, "points": [ { "id": 1, "x": -8, "y": -8, "show_point": false, "highlight_point": false, "highlight_point_color": "#377CF6", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "airport" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 2, "x": 8, "y": -8, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "train_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 3, "x": -4, "y": -4, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "mailbox" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 4, "x": 8, "y": -4, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "city_hall" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 5, "x": -4, "y": 6, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "shopping_cart" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 6, "x": -8, "y": 6, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "hotel" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id":7, "x": 2, "y": 6, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "books" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 8, "x": 8, "y": 6, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "gas_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }], "line_segments": [], "legend_options": { "show_menu": true, "menu_position": "right", "menu_items": [ { "label": "Library", "icon": { "name": "books" } }, { "label": "Post office", "icon": { "name": "mailbox" } } , { "label": "City hall", "icon": { "name": "city_hall" } }, { "label": "Shopping mall", "icon": { "name": "shopping_cart" } }, { "label": "Hotel", "icon": { "name": "hotel" } }, { "label": "Train station", "icon": { "name": "train_station" } } , { "label": "Airport", "icon": { "name": "airport" } }, { "label": "Gas station", "icon": { "name": "gas_station" } } ] }}'></LineGraph ><p>You are currently at the gas station, but you need to get to the shopping mall.</p><ul><li>What are the coordinates for both the gas station and the shopping mall?</li><li>What is the distance between the gas station and the shopping mall?</li></ul> <p><highlight data-color="#666" data-style="italic">Each big square represents `2` miles.</highlight></p>

### #4 of 7:Medium

Find the distance between two points (real world problems)

<LineGraph data-props='{ "options": { "x_min": -10, "y_min": -10, "y_max": 10, "x_max": 10, "cell_size": 20, "x_interval": 1, "y_interval": 1 , "x_skip_interval": 2, "y_skip_interval": 2 }, "points": [ { "id": 1, "x":-8, "y": -8, "show_point": false, "highlight_point": false, "highlight_point_color": "#377CF6", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "airport" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 2, "x": 8, "y": -8, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "train_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 3, "x": -4, "y": -4, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "mailbox" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 4, "x": 8, "y": -4, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "city_hall" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 5, "x": -4, "y": 6, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "shopping_cart" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 6, "x": -8, "y": 6, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "hotel" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 7, "x": 2, "y": 6, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "books" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 8, "x": 6, "y": 6, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "gas_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }], "line_segments": [], "legend_options": { "show_menu": true, "menu_position": "right", "menu_items": [ { "label": "Library", "icon": { "name": "books" } }, { "label": "Post office", "icon": { "name": "mailbox" } } , { "label": "City hall", "icon": { "name": "city_hall" } }, { "label": "Shopping mall", "icon": { "name": "shopping_cart" } }, { "label": "Hotel", "icon": { "name": "hotel" } }, { "label": "Train station", "icon": { "name": "train_station" } } , { "label": "Airport", "icon": { "name": "airport" } }, { "label": "Gas station", "icon": { "name": "gas_station" } } ] }}'></LineGraph ><p>You are currently at the hotel, but you need to get to the airport.</p><ul><li>What are the coordinates for both the hotel and the airport?</li><li>What is the distance between the hotel and the airport?</li></ul><p><highlight data-color="#666" data-style="italic">Each big square represents `2` miles.</highlight> </p>

### #5 of 7:Spicy

Find the distance between two points (real world problems)

<LineGraph data-props='{ "options": { "x_min": -5, "y_min": -5, "y_max": 5, "x_max": 5, "cell_size": 20, "x_interval": 0.5, "y_interval": 0.5, "x_skip_interval": 1, "y_skip_interval": 1 }, "points": [ { "id": 1, "x": -1.5, "y": 4.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#000", "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "graduation_cap" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 2, "x": 3.5, "y": 4.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#000", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "home" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 3, "x": -2.5, "y": 0, "show_point": false, "highlight_point": false, "highlight_point_color": "#000", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "bank" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 4, "x": -4.5, "y": -2.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#000", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "books" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 5, "x": 3.5, "y": -2.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#000", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "mailbox" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 6, "x": 3.5, "y": 0, "show_point": false, "highlight_point": false, "highlight_point_color": "#000", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "kite" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 7, "x": 0, "y": -2.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#000", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "weight_lifter" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 8, "x": -4.5, "y": 1, "show_point": false, "highlight_point": false, "highlight_point_color": "#000", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "shopping_cart" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } ], "legend_options": { "show_menu": true, "menu_position": "right", "menu_items": [ { "label": "Playground", "icon": { "name": "kite" } }, { "label": "City Hall", "icon": { "name": "bank" } }, { "label": "Libray", "icon": { "name": "books" } }, { "label": "Post office", "icon": { "name": "mailbox" } }, { "label": "School", "icon": { "name": "graduation_cap" } }, { "label": "Gym", "icon": { "name": "weight_lifter" } }, { "label": "Home", "icon": { "name": "home" } }, { "label": "Market", "icon": { "name": "shopping_cart" } } ] }}'></LineGraph ><p>You are currently at city hall, but you need to get to the playground.</p><ul><li>What are the coordinates for both city hall and the playground?</li><li>What is the distance between city hall and the playground?</li></ul> <p><highlight data-color="#666" data-style="italic">Each big square represents `1` mile.</highlight></p>

### #6 of 7:Spicy

Find the distance between two points (real world problems)

<LineGraph data-props='{ "options": { "x_min": -5, "y_min": -5, "y_max": 5, "x_max": 5, "cell_size": 20, "x_interval": 0.5, "y_interval": 0.5 , "x_skip_interval": 1, "y_skip_interval": 1 }, "points": [ { "id": 1, "x": 0.5, "y": 2.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#377CF6", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "bank" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 2, "x": -4, "y": -3.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "theater" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 3, "x": 0.5, "y": -3.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "gas_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 4, "x": 0.5, "y":4.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "books" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 5, "x": 3.5, "y": -3.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "police_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 6, "x": -4, "y": 0, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "fire_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 7, "x": 3.5, "y":0, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "museum" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 8, "x": -4, "y": 2.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "mailbox" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }], "line_segments": [], "legend_options": { "show_menu": true, "menu_position": "right", "menu_items": [ { "label": "Bank", "icon": { "name": "bank" } }, { "label": "Theater", "icon": { "name": "theater" } }, { "label": "Gas station", "icon": { "name": "gas_station" } }, { "label": "Library", "icon": { "name": "books" } }, { "label": "Police station", "icon": { "name": "police_station" } }, { "label": "Fire station", "icon": { "name": "fire_station" } }, { "label": "Museum", "icon": { "name": "museum" } }, { "label": "Post office", "icon": { "name": "mailbox" } } ] }}'></LineGraph > <p>You are currently at the bank, but you need to get to the gas station.</p><ul><li>What are the coordinates for both the bank and the gas station?</li><li>What is the distance between the bank and the gas station?</li></ul><p><highlight data-color="#666" data-style="italic">Each big square represents `1` mile.</highlight></p>

### #7 of 7:Spicy

Find the distance between two points (real world problems)

<LineGraph data-props='{ "options": { "x_min": -5, "y_min": -5, "y_max": 5, "x_max": 5, "cell_size": 20, "x_interval": 0.5, "y_interval": 0.5 , "x_skip_interval": 1, "y_skip_interval": 1 }, "points": [ { "id": 1, "x": -4, "y": 4, "show_point": false, "highlight_point": false, "highlight_point_color": "#377CF6", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "graduation_cap" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 2, "x": 3.5, "y": -4, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "train_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 3, "x": -4, "y": -4, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "mailbox" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 4, "x": 4, "y": -2, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "city_hall" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 5, "x": -4.5, "y": 1, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "shopping_cart" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 6, "x": -4, "y": 3, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "hotel" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 7, "x": -4.5, "y": -2.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "books" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 8, "x": 3.5, "y": 3.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "gas_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }], "line_segments": [], "legend_options": { "show_menu": true, "menu_position": "right", "menu_items": [ { "label": "Library", "icon": { "name": "books" } }, { "label": "Post office", "icon": { "name": "mailbox" } } , { "label": "City hall", "icon": { "name": "city_hall" } }, { "label": "Shopping mall", "icon": { "name": "shopping_cart" } }, { "label": "Hotel", "icon": { "name": "hotel" } }, { "label": "Train station", "icon": { "name": "train_station" } } , { "label": "School", "icon": { "name": "graduation_cap" } }, { "label": "Gas station", "icon": { "name": "gas_station" } } ] }}'></LineGraph ></LineGraph ><p>You are currently at the train station, but you need to get to the gas station.</p><ul><li>What are the coordinates for both the train station and the gas station?</li><li>What is the distance between the train station and the gas station?</li></ul> <p><highlight data-color="#666" data-style="italic">Each big square represents `1` mile.</highlight></p>

In summary, finding the distance between two points is a fundamental concept in mathematics and is used in a wide range of real-world applications, including navigation, surveying, construction, physics and engineering, and statistics. Having practice problems on this topic helps students to practice and reinforce the knowledge of this concept and apply it to real-world situations.

Additionally, distance formulas are used in physics and engineering to calculate the distance between two points in space, velocity, and time, as well as in statistics to calculate the...

Show all
Coordinate Plane
6.NS.C.8

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Carmel, CA
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### What teachers are saying about BytelearnWhat teachers are saying

Stephen Abate
19-year math teacher
Carmel, CA
Any math teacher that I know would love to have access to ByteLearn.
Jennifer Maschino
4-year math teacher
Summerville, SC
“I love that ByteLearn helps reduce a teacher’s workload and engages students through an interactive digital interface.”
Rodolpho Loureiro
Dean, math program manager, principal
Miami, FL
“ByteLearn provides instant, customized feedback for students—a game-changer to the educational landscape.”