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?

AsadRehman
Apr 13, 2017

#1**+1 **

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

The area will increase by 5 *twice,* that is 5*5 = 5^{2} = 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 * 4^{2}

The area of △A'B'C' is 4^{2} times bigger than △ABC.

hectictar
Apr 14, 2017