Question

A line segment has endpoints (-4,-6) and (-6,4). Which reflection will produce an image with end points at (4,-6) and (6,4)?

Answer 1

Reflection about x axis: (x, y) ⇒ (x, -y)
Reflection about y axis: (x, y) ⇒ (-x, y)
Reflection about line y = x: (x, y) ⇒ (y, x)
Reflection about line y = -x: (x, y) ⇒ (-y, -x)
Reflection about origin: (x, y) ⇒ (-x, -y)

(-4, -6), (-6, 4) ⇒ (4, -6), (6, 4)
This is a reflection about the y axis because they follow (-x, y).
The x coordinate becomes a negative (in both cases they become positive because two negatives) and the y coordinate stays the same.