Answer:
(4, -4)
Step-by-step explanation:
A point that would map onto itself after a reflection across a line would need to be on the line in the first place.
For example, if you reflected point (2, 2) in the x-axis, the y-coordinate would become negative and so the reflected point would be (2, -2). If the point is not on the line, any reflection across a line will result in a change in at least one of the coordinates of the point.
Given line: y = -x
To find which point is on the given line, simply substitute the x-values of the given points and solve for y.
The answer options have three difference x-values: -4, 0, and 4
Substituting these into y = -x
x = -4 ⇒ y = -(-4) = 4 → (-4, 4)
x = 0 ⇒ y = -(0) = 0 → (0, 0)
x = 4 ⇒ y = -(4) = -4 → (4, -4)
Therefore, the only point that sits on the line is (4, -4) so this is the point that maps onto itself after a reflection in the line y = -x
For proof, see the attached diagram. Each original point is labelled A, B, C and D. When reflected in the line y = -x these points are A', B' C' and D'.
