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Mathematics of Dilations: Exploring Size Changes in Figures

A dilation is a transformation that changes the size of a figure but preserves its shape. In this exercise, Triangle ABC is graphed with an image using a scale factor of 2. The coordinates of the vertices A(0,0), B(4,0), C(0,5) are transformed according to the dilation rules. Explore if increasing the coordinates by 2 or multiplying them by 2 results in similar triangles. A hands-on application of dilations in geometry awaits!

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Mathematics of Dilations: Exploring Size Changes in Figures

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  1. 2.4: Dilations CCSS

  2. A dilationis a transformation that changes the size of a figure but not its shape. The pre-image and the image are always similar shapes. A scale factorfor a dilation with a center at the origin is k, which is found by multiplying each coordinate by k: (a, b)  (ka, kb).

  3. Given Triangle ABC, graph the image Of ABC with a scale factor of 2. (2x, 2y) Image Pre-Image A (1,4) A ‘ (2,8) B (5,1) B ‘(10,2) C (0,0) C ‘ ( 0,0)

  4. Triangle ABC has vertices A ( 0,0) , B( 4,0) , C (0,5). Graph it • If the coordinates of each vertex of ABC are increased by 2, • will the new triangle be similar to triangle ABC (Graph it)? Why or why not? • 2) If the coordinates of each vertex of Triangle ABC are multiplied by 2, • will the new triangle be similar to Triangle ABC (Graph it)? Why or why not?

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