how can you model the effect of a dilation by a scale factor of 3 on the area of a two dimensional shape

Answer 1

To model the effect of a dilation by a scale factor of 3 on the area of a two-dimensional shape, you need to square the scale factor and multiply it by the original area.

Let's say the original area of the shape is represented by A.

The scale factor is 3, so when you dilate the shape by a scale factor of 3, the new area, A', is given by:

A' = (3^2) * A
= 9 * A

Therefore, the new area, A', will be 9 times the original area A when the shape is dilated by a scale factor of 3.