John says the transformation rule (x, y) (x + 4, y + 7) can be used to describe the slide of the pre-image (4, 5) to the image (0, –2). What was his error?

Answer:

John applied the transformation rule to the image instead of the pre-image. If you apply the rule (x + 4, y + 7) to the pre-image (4, 5), the resulting image should be (8, 12). To get from (4, 5) to (0, -2), the rule should actually be (x - 4, y - 7).