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:

The preimage is the point you start with. To check the transformation rule, substitute the values of the coordinates (4, 5) into the rule. You get (4, 5) → (44, 57). Simplify to get (4, 5) → (8, 12). This is the image. Instead the rule was applied to the image. This is the source of the error.