First, find the distance AB by the formula:
[tex]AB=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}.[/tex]
If A(0,-7) and B(8,8), then
[tex]AB=\sqrt{(8-0)^2+(8-(-7))^2}=\sqrt{8^2+15^2}=\sqrt{64+225}=\sqrt{289}=17.[/tex]
Dilating polygon ABCD by a scale factor of 2 with the center of dilation at the origin to create polygon A′B′C′D′, you increase the distance AB twice, A'B'=2AB. Thus, A'B'=2·17=34 units.
Answer: AB=17 units, A'B'=34 units.
