Sophia is dilating a figure. One of her pre-image points with coordinates (-3, 5) has an image with coordinates (-9, 15). If one of the other image points has coordinates (3, 1), what are the coordinates of its pre-image point?

Question

mathmate · Answer

First you need to find out if the dilation is about the origin by checking the ratio of the pre-image and image coordinates: i.e. calculate kx=x'/x, ky= y'/y.  If kx=ky, then the dilation is about the origin, call this factor k.

If the dilation is about the origin, you can multiply the coordinates of any pre-image point by k to get the image.