Question

Polygon ABCD is dilated by a scale factor of 2 with the center of dilation at the origin to create A'B'C'D'. If the endpoints of Line AB are located at (0,-7) and (8,8) what is the length of A'B'? Use the distance formula to help you decide.

Answer 1

The distance formula is given by $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Take point A(0, -7) as (x₁, x₂) and point B(8, 8) as (y₁, y₂)

Distance AB = $\sqrt{(8-0)^2+(8--7)^2}$
Distance AB = $\sqrt{8^2+15^2}$
Distance AB = $\sqrt{289}$
Distance AB = 17

The line AB is dilated to A'B' by scale factor of 2, it means the length of the line is multiplied by 2

Distance A'B' = 2 × 17 = 34 units