Polygon abcd is dilated by a scale factor of 2 with the center of dilation at the origin to create polygon a′b′c′d′. if the endpoints ab of are located at (0, -7) and (8, 8), what is the length of a'b'? use the distance formula to you decide: d = √(x₂-x₁)²+(y₂-y₁)²

Answer is 34 units.

Figures are defined by pre-image and image, so the image would be the dilation while the pre-image is the original figure. So with the preimage being larger, the dilation has to be a fraction less than 1.

Here preimage is smaller, and image is bigger hence scale factor is greater than 1 i.e. 2

Due to dilation, a similar figure is obtained without disturbing the shape of pre image.

Hence AB will becomes A'B' with length = scale factor x AB

= 2x AB.

We can find out AB using distance formula

AB = √(x₂-x₁)²+(y₂-y₁)²

=√(8-0)²+(8+7)²=√(64+225) =√289 = 17

Hence Length of A'B' = 2(17) = 34 units.