Given:
Consider the two points are B(2,3) and B'(-4,-6).
Center of dilation is the origin.
To find:
The scale factors of this dilation that transformed B into B'.​
Solution:
If a figure dilatated by scale factor k and center of dilation is the origin, then
[tex](x,y)\to (kx,ky)[/tex]
It means, the point after dilation is
[tex](x',y')=(kx,ky)[/tex]
where, k is the scale factor.
[tex]k=\dfrac{x'}{x}[/tex]
x-coordinate of image is -4 and x-coordinate of original point is 2.
[tex]k=\dfrac{-4}{2}[/tex]
[tex]k=-2[/tex]
Therefore, the scale factor is -2. It means, the point and image lie on the opposite sides of center of dilation.
