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

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

Mercury · Answer

Easiest way to check who is right: take the original point (-2,-4), apply each person's rule, and see which one gets you to N(2,4)

for example, using Raheem's: does multiplying the x and y coordinates by -1 get you from (-2,-4) to (2,4)?