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Find the distance between the points (6,7)(6,7) and (2,10)(2,10).\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline______ units

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Q. Find the distance between the points (6,7)(6,7) and (2,10)(2,10).\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline______ units
  1. Identify Coordinates and Formula: Identify the coordinates of the two points and the distance formula.\newlineThe distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) in a plane is given by the formula:\newlineDistance =((x2−x1)2+(y2−y1)2)= \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}\newlineHere, (x1,y1)=(6,7)(x_1, y_1) = (6, 7) and (x2,y2)=(2,10)(x_2, y_2) = (2, 10).
  2. Calculate Coordinate Differences: Calculate the differences in the x-coordinates and y-coordinates.\newlineDifference in x-coordinates: (x2−x1)=(2−6)=−4(x_2 - x_1) = (2 - 6) = -4\newlineDifference in y-coordinates: (y2−y1)=(10−7)=3(y_2 - y_1) = (10 - 7) = 3
  3. Square Coordinate Differences: Square the differences found in Step 22.\newlineSquare of difference in x-coordinates: (−4)2=16(-4)^2 = 16\newlineSquare of difference in y-coordinates: (3)2=9(3)^2 = 9
  4. Add Squares of Differences: Add the squares of the differences.\newlineSum of squares: 16+9=2516 + 9 = 25
  5. Find Distance: Take the square root of the sum of squares to find the distance.\newlineDistance = 25=5\sqrt{25} = 5

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