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
[tex]P(x,y)\to P'(kx,ky)[/tex]
Let the scale factor for the given problem be k. So,
[tex]A(18,9)\to A'(18k,9k)[/tex]
On comparing A'(18k,9k) and A'(6,3), we get
[tex]18k=6\text{ and }9k=3[/tex]
[tex]k=\dfrac{6}{18}\text{ and }k=\dfrac{3}{9}[/tex]
[tex]k=\dfrac{1}{3}\text{ and }k=\dfrac{1}{3}[/tex]
Therefore, the scale factor is [tex]\dfrac{1}{3}[/tex].
