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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?

2 Answers

3 votes

I think it's B hope this helps out


User Frank Nielsen
by
8.3k points
5 votes

Answer:

The scale factor of the dilation is
(1)/(5).

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=(2)/(10)=(1)/(5)

Therefore the scale factor of the dilation is
(1)/(5).

User Pseudoramble
by
7.6k points