Question

A line segment has endpoints at (–1, 4) and (4, 1). Which reflection will produce an image with endpoints at (–4, 1) and (–1, –4)?

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

Answer 1

Reflection across the line y = −x.

Reason: Reflection across y = −x sends (x,y) → (−y,−x). Applying this:
(-1, 4) → (−4, 1)
(4, 1) → (−1, −4),
which matches the given image points.