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A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 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
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Explanation:

The transformations of the end points are:

       Preimage         Image

The means that, for every end point, the x-coordinate changes the sign and the y-coordinate remains unchanged.

That rule is:

Keeping the y-coordinate and changing the sign of the x-coordinate is a reflection across the y -axis. It is like a mirror image, where the mirror is placed along the y-axis. The figure keeps the same distance from the y-axis (the mirror) but changes sides, which is represented by the change of x to - x,  while the altitude (the y-coordinate) keeps unchanged.