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# DeMarco draws PQR with vertices P(−4, 2) , Q(2, 2) , and R(2, −6) . Then he dilates the triangle with a scale factor of 5 to create P′Q′R′

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DeMarco draws △PQR with vertices P(−4, 2), Q(2, 2), and R(2, −6). Then he dilates the triangle with a scale factor of 5 to create △P′Q′R′. How are the areas of the triangles related?

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When you dilate the triangle, you increase two dimensions by 5.

The area will increase by 5 twice, that is 5*5 = 52 = 25

So, the area of △P′Q′R′ is 25 times bigger than the area of △PQR.

Here is an example:

△ABC has a base of 3 units and a height of 6 units.

It is dilated by a scale factor of 4.

△A'B'C' has a base of 3*4 units and a height of 6*4 units.

area of △ABC = (1/2)(3)(6) = 9

area of △A'B'C' = (1/2)(3*4)(6*4) = 9 * 4  * 4 = 9 * 42

The area of △A'B'C' is 42 times bigger than △ABC.

hectictar  Apr 14, 2017

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