Math Playground
Geometry

Reflection

Flip across a line — left becomes right, distances stay the same.

Reflection flips a shape over a line — the mirror line (or axis). The image is the same size and shape, just back-to-front, like your face in a mirror.

Flip the shape
Flip: in the y-axis

Each point (x, y) maps to (−x, y). Distances and angles stay the same — only the handedness flips.

original image

What reflection keeps and changes

  • Kept: lengths, angles, area — the image is *congruent* to the original.
  • Changed: orientation flips (clockwise becomes anticlockwise) — a left hand reflects to a right hand.
  • Every point and its image are the same distance from the mirror line, on opposite sides; the mirror line is the perpendicular bisector of the join.
  • Points on the mirror line don't move — they're fixed.
Your turn

Reflect the point (3, 2) in the y-axis. Where does it land?

Watch out

A reflection is not the same as a rotation of 180°. Both 'turn the shape around', but a reflection reverses orientation (mirror image) while a half-turn doesn't. Check a lopsided shape like the 'F' above to tell them apart.