∆abc is transformed with the center of dilation at the origin. pre-image: ∆abc with vertices a(2, 5), b(6, 10), c(9, −1) image: ∆a'b'c' with vertices a' (0.5, 1.25), b' (1.5, 2.5), c' (2.25, −0.25) what is the scale factor of the dilation that maps the pre-image to the image?

1/4

Step-by-step explanation:

We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(2, 5), B(6, 10) and C(9, −1) to the image triangle A'B'C' with vertices A' (0.5, 1.25), B' (1.5, 2.5), C' (2.25, −0.25).

Center of dilation is at the origin.

To find the scale factor, we will divide the corresponding vertices of the image and pre-image.

A(2, 5) ---> A' (0.5, 1.25) =

B(6, 10) ---> B' (1.5, 2.5) =

C(9, −1) ---> C' (2.25, −0.25) =

Therefore, the scale factor of the dilation is 1/4.