Question

Triangle ABC has vertices A(5,3), B(3,7), and C(1,4). Triangle ABC is dilated and the vertices of the image are A'(2.5, 1.5), B'(1.5, 3.5), and C'(0.5,2). The Center of dilation is the origin.

What is the scale factor of the dilation?

A. 0.25

B. 0.5

C. 2

D. 4​

Answer 1

B. 0.5

Step-by-step explanation

Triangle ABC has vertices A(5,3), B(3,7), and C(1,4).

After triangle ABC is dilated about the origin, the vertices of the image are

A'(2.5, 1.5), B'(1.5, 3.5), and C'(0.5,2).

Let k be the scale factor of the dilation, then

`(x,y)\to (kx,ky)`

We can then use a point and it's corresponding image to find k.

`A(5,3)\to A'(5k,3k)`

This implies that

`A'(5k,3k) = A'(2.5,1.5)`

`5k = 2.5`

`k = (2.5)/(5)`

`k = (1)/(2) = 0.5`

The scale factor is 0.5