Symmetry Explorer — play with mirror lines
Drag a shape by its corners and watch its mirror twin copy every move, flipped across the line.
Symmetry means one half of a picture is the mirror image of the other. Butterflies, snowflakes, faces and folded-paper cutouts all obey this rule. In this explorer a shape sits on one side of a red mirror line, and its twin sits on the other side. However you drag the orange corners, the twin copies the move in reverse — always exactly as far from the line as the original.
In Free draw, click anywhere on the board to add a dot, drag dots to move them, and watch the mirror keep up. This is how butterfly wings, snowflakes and folded-paper cutouts work.
How to play
Pick a starting shape, then choose a vertical, horizontal or diagonal mirror line and drag the orange dots. Switch to Free draw to place your own dots and invent a shape of your own, then clear them and start again whenever you like.
What you learn
You build an instinct for reflection: points on the line stay put, points near it have twins near it, and distance to the mirror is always preserved. That instinct is the foundation for symmetry questions in geometry — and for spotting balanced designs everywhere else.
Want more? Browse the whole Interactive Geometry Lab for nine hands-on math toys, or build a personalised math adventure for your child with the free Game Builder. Everything is free, with no sign-up.
✓ Last checked November 2, 2026 — we re-test this tool every week to make sure it still works.