Question

Analyzing Student Work
John says the transformation rule (x, y) Right-arrow (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 1

John used the wrong translation vector (wrong signs).
Applying his rule (x, y) → (x+4, y+7) to (4,5) gives (8,12), not (0,−2). The displacement from (4,5) to (0,−2) is (−4, −7), so the correct rule is (x, y) → (x−4, y−7) (or (x+ (−4), y+ (−7))).