Question

When the point (-1,3) is dilated with the center of dilation at the origin, The image of the point is (-4,12)

What is the scale factor of this dilation?

Answer 1

The scale factor is the number all sides of the figure are multiplied by in order to reach the desired dilation. In this case that would be 4.

Answer 2

The scale factor of this dilation is 4.

Explanation:

If the image of a point P(x,y) after the dilated with the center of dilation at the origin is P'(x',y'), then the scale factor of dilation is

`k=(x')/(x)=(y')/(y)`

The point (-1,3) is dilated with the center of dilation at the origin, the image of the point is (-4,12).

It means
`x=-1,y=3,x'=-4,y'=12`

The scale factor of this dilation is

`k=(-4)/(-1)`

`k=4`

Therefore the scale factor of this dilation is 4.