Question

A triangle with vertices at A(20, –30), B(10, –15), and C(5, –20) has been dilated with a center of dilation at the origin. The image of B, point mc017-1.jpg, has the coordinates (2, –3). What is the scale factor of the dilation?

Answer 1

I think it's B hope this helps out

Answer 2

Answer:

The scale factor of the dilation is $\frac{1}{5}$.

Step-by-step 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

$P(x,y)\rightarrow P'(kx,ky)$

$B(10,-15)\rightarrow B'(k(10),k(-15))$

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

$B'(10k,-15k)=B'(2,-3)$

On comparing both sides, we get

$10k=2$

$k=\frac{2}{10}=\frac{1}{5}$

Therefore the scale factor of the dilation is $\frac{1}{5}$.