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?

4
0.25
-4
-0.25

Answer 1

Answer: The correct option is

(C) -4.

Step-by-step explanation: Given that a point (-1, 3) is dilated with the center of dilation at the origin and the image of the point is (4,-12).

We are to find the scale factor of the dilation.

We know that

when a point (a, b) is dilated about the origin to another point (c, d), then its scale of dilation is given by

`s=(c)/(a)=(d)/(b).`

Therefore, for the given dilation, the scale factor of dilation is given by

`s=(4)/(-3)=(-12)/(3)=-4.`

Thus, the required scale factor is -4.

Option (C) is CORRECT.

Answer 2

-4

Explanation:

When the dilation center is the origin, the dilation factor is the ratio of dilated coordinates to original coordinates: 4/-1 = -12/3 = -4.