Question

Point A' is a dilation of point A. Find the scale factor: A (18, 9) A' (6, 3)

Answer 1

Given:

Point A'(6,3) is a dilation of point A(18,9).

To find:

The scale factor.

Solution:

We know that, if a point P is dilated by factor k and origin is the center of dilation, then

$P(x,y)\to P'(kx,ky)$

Let the scale factor for the given problem be k. So,

$A(18,9)\to A'(18k,9k)$

On comparing A'(18k,9k) and A'(6,3), we get

$18k=6\text{ and }9k=3$

$k=\dfrac{6}{18}\text{ and }k=\dfrac{3}{9}$

$k=\dfrac{1}{3}\text{ and }k=\dfrac{1}{3}$

Therefore, the scale factor is $\dfrac{1}{3}$.