What Is a Reflection?

How a reflection behaves

Reflection preserves lengths and angle measures, so the image is congruent to the original. What changes is orientation: the figure becomes a mirror image rather than a turned copy.

This page keeps the line of reflection and the paired points on screen together so the flip can be justified by geometry, not just by appearance.

If a point is 4 units above a horizontal mirror line, its image must be 4 units below that line. The segment joining the point and its image crosses the mirror at a right angle and is cut in half there. Those two tests explain the mirror image more clearly than simply saying it looks reversed.

• A reflection flips a figure across a line.
• The line of reflection is the perpendicular bisector of the segment joining any point to its reflected image.
• Reflection is a rigid motion, so side lengths and angle measures are preserved.
• Orientation reverses under reflection, which is why letters and ordered shapes can look mirrored.

Where reflections help

• Use reflection when finding images across the x-axis, y-axis, y = x, or another mirror line.
• Use it in symmetry problems where a figure matches itself across a line.
• Use it in coordinate proofs that rely on equal distance from a line or on perpendicular bisector structure.

Reflection checks to make

• Do not guess the reflected point by eye without checking equal perpendicular distance from the mirror line.
• Do not confuse reflection with rotation just because the image looks repositioned.
• Do not forget that the line of reflection sits midway between corresponding points, not on one side of them.