Question

If rectangle ABCD is dilated to rectangle A'B'C'D', being centered at the origin, what is the scale factor used here?

• A. 3
• B. 2
• C. $\frac{1}{2}$
• D. $\frac{1}{3}$

Answer 1

The correct option is A 3

We know,
The scale factor of a dilation is the ratio of the length of the dilated image to the corresponding length in the original figure.


In the red figure:
The side connecting points A' and B' is = 6 - (-6) = 6 + 6 = 12 units long.

In the black figure:
The side connecting points A and B is = 2 - (-2) = 2 + 2 = 4 units long.

Here, the rectangle ABCD is dilated to the rectangle A'B'C'D', centered at the origin.

$\text{So, the scale factor is}=\frac{12}{4}=3$

∴ Option (A) is correct.