Answer:
The scale factor of the dilation is
.
Explanation:
Given information: A triangle with vertices at A(20, –30), B(10, –15), and C(5, –20). The center of dilation at the origin. The image of B has the coordinates (2, –3).
If a figure dilated with a center of dilation at the origin and scale factor k, then


Since the image of B has the coordinates (2, –3), therefore

On comparing both sides, we get


Therefore the scale factor of the dilation is
.