To solve these problems, students need to identify the coordinates of the vertices of the given triangle. The center of dilation is the origin, which means to find the new coordinates of the triangle students have to multiply the coordinate of the original triangle by the scale factor. For example, if the three vertices of a triangle are (2,1),(2,5) and (3,4) and the scale factor is 2 with the origin as the center of dilation then the vertices of the triangle after dilation are (4,2), (4,10) and (6,8).

Dilate triangles on a coordinate grid

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In 8th Grade, students learn about dilation and how to plot the point on a coordinate plane after the dilation. Some student face difficulties while dilating the triangle on a coordinate grid. Teachers can provide “Dilate triangles on a coordinate grid worksheet” to their students. This worksheet can help them to overcome difficulties. In this worksheet, each question has a triangle on a coordinate grid and a <a href="https://www.bytelearn.com/math-topics/scale-factor" target="_blank" class="backlink">scale factor</a> of dilation, students are asked to plot the triangle after dilation.

Firstly, students should be able to define what a transformation is. A transformation is a change in the position, shape, or size of a geometric figure. There are four basic types of transformations: translation, reflection, rotation, and dilation.&nbsp;Students should understand the properties of each type of transformation. For example, a translation is a movement of a figure without changing its shape or size, while a reflection is a transformation that flips a figure across a line of symmetry.&nbsp;Next, students should be able to perform transformations on geometric figures. They should be able to use coordinate notation and describe the effects of transformations on the coordinates of points.&nbsp;Finally, students should be able to solve problems involving transformations. They should be able to use transformations to determine congruence, symmetry, and similarity of geometric figures.&nbsp;In summary, understanding transformations is a key aspect of geometry for grade 8 students.

<h2 style="text-align:justify;">8th Grade Course Summary&nbsp;</h2>&nbsp;In 8th grade math, students are introduced to high-value concepts and expand their knowledge of operations and execution of these concepts. Here is a brief overview of the 8th Grade Math Course:&nbsp;&nbsp;<h2><a href="https://www.bytelearn.com/math-grade-8/Exponents">Exponents</a></h2><h2><a href="https://www.bytelearn.com/math-grade-8/linear-relationships-and-functions">Linear Relationships And Functions</a></h2><h2><a href="https://www.bytelearn.com/math-grade-8/Scientific-Notation">Scientific Notation</a></h2>&nbsp;

grade 8

The 8th-grade math curriculum has been designed to help students advance mathematically, particularly in the areas of algebraic equations. They focus on three core areas; reasoning and formulating, describing and deriving relationships, and analyzing two and three-dimensional figures.&nbsp; &nbsp;Students are also taught to expand their understanding of proportional relationships. They also learn the importance of solutions and application to single linear equations. They work on various models with bivariate data and learn to make the necessary predictions. Functions open a new arena for them to learn high-value functions in high school. They continue by studying with measurement and movement of figures, lines, and angles with two and three-dimensional figures.&nbsp;

Transformations

Transformations are a fundamental concept in geometry that is important for grade 8 students to understand. According to the Common Core Standards for Math, students should be able to understand the properties of transformations and use them to solve problems. &nbsp;

Students will then explore how to perform each type of transformation and how they affect the shape and position of a figure. They will also learn how to describe a transformation using coordinates and matrices. The lesson includes interactive activities and opportunities for student collaboration, and assessments to ensure mastery of the concept. By the end of this lesson, students will have a solid foundation in transformation geometry that they can build upon in future math classes.

8th Grade Math Transformations Lesson Plan

This 8th grade math transformations lesson plan aligns with the Common Core State Standards for Mathematics. Students will learn about the different types of transformations, including translations, reflections, rotations, and dilations. The lesson begins with an introduction to basic geometric vocabularies, such as congruence, symmetry, and transformation.&nbsp;

Teachers can also assign these math practice problems to their students to assess their knowledge of this topic.

Transformations Problems is a set of exercises designed for 8th grade students in accordance with the Common Core Standards for Mathematics. These problems focus on geometric transformations, including translations, reflections, rotations, and dilations. By practicing these problems, students can improve their understanding of how to perform and describe these transformations, and how to use them to solve problems.&nbsp;&nbsp;The problems aim to develop students' proficiency in applying geometric transformations to solve real-world problems and to enhance their visualization skills. Through these problems, students can deepen their knowledge of geometric concepts, such as congruence and similarity, and develop their ability to reason abstractly and quantitatively. Teachers can use these problems to reinforce classroom instruction, provide additional practice, and assess students' mastery of the key concepts and skills related to geometric transformations.

Teachers can also assign this system of equations unit quiz to their students to assess their knowledge of this topic.

Transformations Quizzes is a series of assessments designed for 8th grade students in accordance with the Common Core Standards for Mathematics. These quizzes focus on geometric transformations, including translations, reflections, rotations, and dilations. By taking these quizzes, students can improve their understanding of how to perform and describe these transformations, and how to use them to solve problems. The quizzes aim to assess students' mastery of the key concepts and skills related to transformations and to provide feedback to teachers on areas where students may need additional support or instruction. Through these quizzes, teachers can monitor student progress, identify areas for improvement, and tailor their instruction to meet the individual needs of each student.

Dilate Triangle `ABC` with a scale factor of `3` to create Triangle `DEF`.Use the origin as the center of dilation.<selectivedisplay data-props='{"show_in_create":true,"show_in_problem_qa": true}'> <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": 1, "y": -1, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "A", "label_position":"left" }, { "id": 2, "x": 3, "y": -1, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "B" }, { "id": 3, "x": 2, "y": -3, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "C" } ], "line_segments": [ { "first_point_id": 1, "second_point_id": 2, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 2, "second_point_id": 3, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 3, "second_point_id": 1, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" } ]}'></LineGraph ></selectivedisplay>

Math

Dilate Triangle `QRS` with a scale factor of `4` to create Triangle `TUV`.Use the origin as the center of dilation.<selectivedisplay data-props='{"show_in_create":true,"show_in_problem_qa": true}'> <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": 0, "y": 2, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "Q" }, { "id": 2, "x": 2, "y": -1, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "R" }, { "id": 3, "x": 1, "y": 0, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "S", "label_position":"below" } ], "line_segments": [ { "first_point_id": 1, "second_point_id": 2, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 2, "second_point_id": 3, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 3, "second_point_id": 1, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" } ]}'></LineGraph ></selectivedisplay>

Dilate Triangle `QRS` with a scale factor of `2.5` to create Triangle `TUV`.Use the origin as the center of dilation.<selectivedisplay data-props='{"show_in_create":true,"show_in_problem_qa": true}'> <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": 4, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "Q" }, { "id": 2, "x": 4, "y": -2, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "R" }, { "id": 3, "x": -2, "y": 0, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "S" } ], "line_segments": [ { "first_point_id": 1, "second_point_id": 2, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 2, "second_point_id": 3, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 3, "second_point_id": 1, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" } ]}'></LineGraph ></selectivedisplay>

Dilate Triangle `ABC` with a scale factor of `0.5` to create Triangle `DEF`.Use the origin as the center of dilation.<selectivedisplay data-props='{"show_in_create":true,"show_in_problem_qa": true}'> <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": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "A" }, { "id": 2, "x": 10, "y": 6, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "B" }, { "id": 3, "x": 4, "y": 2, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "C", "label_position":"below" } ], "line_segments": [ { "first_point_id": 1, "second_point_id": 2, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 2, "second_point_id": 3, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 3, "second_point_id": 1, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" } ]}'></LineGraph ></selectivedisplay>

Dilate Triangle `QRS` with a scale factor of `1.5` to create Triangle `TUV`.Use the origin as the center of dilation.<selectivedisplay data-props='{"show_in_create":true,"show_in_problem_qa": true}'> <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": 6, "y": 6, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "Q" }, { "id": 2, "x": 4, "y": -6, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "R" }, { "id": 3, "x": -4, "y": 0, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "S" } ], "line_segments": [ { "first_point_id": 1, "second_point_id": 2, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 2, "second_point_id": 3, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 3, "second_point_id": 1, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" } ]}'></LineGraph ></selectivedisplay>

Dilate Triangle `ABC` with a scale factor of `3/4` to create Triangle `DEF`.Use the origin as the center of dilation.<selectivedisplay data-props='{"show_in_create":true,"show_in_problem_qa": true}'> <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, "show_major_and_minor_grid_lines":true }, "points": [ { "id": 1, "x": 4, "y": 4, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "A" }, { "id": 2, "x": -4, "y": 0, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "B" }, { "id": 3, "x": -2, "y": -2, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "C" } ], "line_segments": [ { "first_point_id": 1, "second_point_id": 2, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 2, "second_point_id": 3, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 3, "second_point_id": 1, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" } ]}'></LineGraph ></selectivedisplay>

Dilate Triangle `ABC` with a scale factor of `2.5` to create Triangle `DEF`.Use the origin as the center of dilation.<selectivedisplay data-props='{"show_in_create":true,"show_in_problem_qa": true}'> <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, "show_major_and_minor_grid_lines":true }, "points": [ { "id": 1, "x": 1, "y": 2, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "A" }, { "id": 2, "x": -2, "y": 0, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "B" }, { "id": 3, "x": -1, "y": -1, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "C" } ], "line_segments": [ { "first_point_id": 1, "second_point_id": 2, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 2, "second_point_id": 3, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 3, "second_point_id": 1, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" } ]}'></LineGraph ></selectivedisplay>

Dilate Triangle `QRS` with a scale factor of `1/2` to create Triangle `TUV`.Use the origin as the center of dilation.<selectivedisplay data-props='{"show_in_create":true,"show_in_problem_qa": true}'> <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, "show_major_and_minor_grid_lines":true }, "points": [ { "id": 1, "x": -2, "y": 4, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "Q" }, { "id": 2, "x": 3, "y": 2, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "R" }, { "id": 3, "x": 0, "y": -2, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "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, "label": "S" } ], "line_segments": [ { "first_point_id": 1, "second_point_id": 2, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 2, "second_point_id": 3, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 3, "second_point_id": 1, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" } ]}'></LineGraph ></selectivedisplay>

Dilate Triangles On A Coordinate Grid Worksheet

8 problems

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