Question

Four students are trying to find the rule that translates point N(–2, –4) to N prime (2, 4). Each student’s reasoning is shown below.

Raheem: The rule is (x times (negative 1), y times (negative 1)) because Negative 2 times (negative 1) = 2 and Negative 4 times (negative 1) = 4.
Casey: The rule is (x + 2, y + 4) because the image is (2, 4).
Andrew: The rule is (x + 4, y + 0) because the coordinates are opposites.
Lo: The rule is (x + 4, y + 8) because Negative 2 + 4 = 2 and Negative 4 + 8 = 4.

Which student is correct?
Raheem
Casey
Andrew
Lo

Answer 1

Lo.

The translation vector is (2 - (−2), 4 - (−4)) = (4, 8), so the rule is (x + 4, y + 8).
Raheem's rule (−x, −y) also sends (−2, −4) to (2, 4) but is a reflection (not a translation). Casey and Andrew are incorrect.