Question

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?

Answer 1

The dilation factor Sophia is using appears to be
  (image coordinate)/(original coordinate) = -9/-3 = 15/5 = 3

Then the problem tells us
  (pre-image point)×3 = (3, 1)
so we conclude
  (pre-image point) = (3, 1)/3 = (1, 1/3)