Question

What is the scale factor of the dilation?

Answer 1

Answer: C.
`(1)/(3)`

Explanation:

The coordinates of vertices of any figure(pre-image) (x,y) after dilation with scale factor 'k' will become : (kx,ky)→ Image.

such that
`k=\frac{\text{coordinate of x in image}}{\text{coordinate of x in pre-image}}`

From the given figure, the coordinates of point C (in pre-image)=(-6,-6)

And the coordinates of image = (-2,-2)

`\\\\\Rightarrow\ k=(-2)/(-6)=(1)/(3)`

Hence, the scale factor of the dilation =
`(1)/(3)`

Answer 2

1/3

Explanation:

To find the scale factor write a ratio from the side length of the small triangle to a corresponding side length of the large triangle.

C'B' has the distance 3 units and CB has the distance 9 units.

The ratio then is 3/9 = 1/3. So the scale factor is 1/3 because it is shrinking the larger triangle to the smaller as shown by the ' marks on the letters.