Question

A point has the coordinates (0, k).

Which reflection of the point will produce an image at the same coordinates, (0, k)?

a reflection of the point across the x-axis
a reflection of the point across the y-axis
a reflection of the point across the line y = x
a reflection of the point across the line y = –x

Answer 1

Reflection across the y-axis.

Reason: reflecting (x,y) across the y-axis gives (-x,y), so (0,k) → (0,k). (Reflections across the x-axis give (0,−k), across y=x give (k,0), across y=−x give (−k,0). Only when k=0 do all reflections leave the point unchanged.)