What identifies an axis as a line of reflection?

• A. Two ordered pairs have equal coordinates.
• B. Points lie on a circle centered at the origin.
• C. Two ordered pairs have opposite x-coordinates or opposite y-coordinates.
• D. The line has slope zero.

Answer: (C)

A line of reflection works like a mirror. The image of a point is placed so that the line sits exactly between the point and its image, and the line is perpendicular to the segment joining them. In coordinates, this means the coordinates of a point and its image show a symmetry across the axis: if the axis is vertical, the x-values line up symmetrically around that line (their x-coordinates are opposite in relation to the axis), while the y-values stay the same. If the axis is horizontal, the y-values are opposite with respect to the axis and the x-values stay the same. So, a pair of corresponding points will have opposite x-coordinates or opposite y-coordinates depending on the direction of the axis. That’s why this describes a reflection axis correctly.

For comparison: the idea of equal coordinates would place both points on top of each other, not a mirror image. A circle centered at the origin isn’t about reflection symmetry. A line with slope zero is just a horizontal line, but a reflection axis can have any slope, not only horizontal.