Reflections

Geometry · Axiom Academy

Flipping shapes over a line of reflection A reflection sends every point straight across a fixed line to a mirror point on the other side. The line of reflection acts exactly like a mirror. Every point and its image are equidistant from the line (the two equal tick marks) The line is the perpendicular bisector of the segment connecting a point to its image (the right-angle mark) Points on the line of reflection don't move Reflecting a whole figure just means applying one rule to every vertex. Watch a triangle flip over the x-axis — each corner drops straight across the mirror to its image. That single flip is one of four standard rules. Reflecting over the coordinate axes and the diagonals y = x and y = −x each has its own coordinate rule: x stays the same, y changes sign y stays the same, x changes sign Swap AND negate both coordinates The x-axis is the mirror. A point above it lands the same distance below it, directly underneath — its x-coordinate is untouched and its y-coordinate flips sign. The x-axis acts as the mirror line Example 1: Reflect over the x-axis Reflect point over the x-axis. The x-coordinate stays 3, but y changes from 7 to −7. Now the y-axis is the mirror. Each point swings horizontally to the same distance on the other side — its y-coordinate is untouched and its x-coordinate flips sign. The y-axis acts as the mirror line Example 2: Reflect a Triangle over the y-axis Triangle PQR has vertices . Reflect it over the y-axis.

This is the written version of the interactive lesson above. See the full Geometry course.