The origin is often used as the center of dilation. If you are dilating a figure centered at the origin, you can multiply the coordinates of the points in the preimage by the scale factor to determine the points in the image.
Given a scale factor of k, the transformation is given by
[tex](x,y)\rightarrow(kx,ky)[/tex]
On our problem, we want to perform a dilation at (-2, 4) with a scale factor of 2, therefore, we have
[tex](-2,4)\rightarrow(-2\cdot2,4\cdot2)=(-4,8)[/tex]
After the dilation the coordinates are (-4, 8).
