**Questions**: A quadrilateral with vertices at A(4, –4), B(4, –16), C(12, –16), and D(12, –4) has been dilated with a center at the origin. The image of D, point D, has coordinates (36, –12). What is the scale factor of the dilation?

1/9 1/3 3 9

**Answer**: Let’s explain step by step;

Given a quadrilateral with vertices at A(4, -4), B(4, -16), C(12, -16), and D(12, -4) has been dilated with a center at the origin. The image of D i.e coordinates of D after dilation are (36,-12).

We need to find the scale factor of dilation.

We can calculate the new coordinates after dilation as follows.

(a,b) → (ma,mb)

As image of D given i.e

D(12,-4) → D'(36,-12)

⇒ 12 → 12m i.e 12m=36 ⇒ m=3

and -4 → -4m i.e -4m=-12 ⇒ m=3

hence, scale factor of the dilation is 3