To determine the post image coordinates after a dilation centered about the origin, we will simply multiply each of the coordinates by the given scale factor of 1/3.
Let's start with Point A.
[tex](-12\times\frac{1}{3},24\times\frac{1}{3})\Rightarrow(-4,8)[/tex]
The post image coordinate of A is at (-4, 8).
Moving on to Point B.
[tex](-30\times\frac{1}{3},0\times\frac{1}{3})\Rightarrow(-10,0)[/tex]
The post image coordinate of B is at (-10, 0).
Lastly to Point C.
[tex](-36\times\frac{1}{3},36\times\frac{1}{3})\Rightarrow(-12,12)[/tex]
The post image coordinate of C is at (-12, 12).
