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:

-4

Step-by-step 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.

Answer 2

Answer:  The correct option is

(C) -4.

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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

$s=\dfrac{c}{a}=\dfrac{d}{b}.$

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

$s=\dfrac{4}{-3}=\dfrac{-12}{3}=-4.$

Thus, the required scale factor is -4.

Option (C) is CORRECT.