Question

∆ABC is transformed with the center of dilation at the origin.

Pre-image: ∆ABC with vertices A(−3, 4), B(−1, 12), C(4, −2)
Image: ∆A'B'C' with vertices A' (−0.6, 0.8), B' (−0.2, 2.4), C' (0.8, −0.4)
What is the scale factor of the dilation that maps the pre-image to the image?

Answer 1

1/5

Explanation:

We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(−3, 4), B(−1, 12) and C(4, −2) to the image triangle A'B'C' with vertices A' (−0.6, 0.8), B' (−0.2, 2.4) and C' (0.8, −0.4).

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 (−3, 4) ---> A' (−0.6, 0.8) =
`(-0.6)/(-3) , (0.8)/(4)=((1)/(5) , (1)/(5))`

B(−1, 12) ---> B' (−0.2, 2.4) =
`(-0.2)/(-1) , (2.4)/(12) = ((1)/(5) , (1)/(5))`

C(4, −2) ---> C' (0.8, −0.4) =
`(0.8)/(4) , (-0.4)/(-2) = ((1)/(5) , (1)/(5))`

Therefore, the scale factor of the dilation is 1/5.