Two Mirrors

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 18 of 61.

Reflect a shape in one mirror and then in a second, parallel mirror, and the shape ends up flipped twice, so it faces the original way again. The two flips together are a single slide: at right angles to the mirrors, and twice the gap between them.

$P reflected in x = 0 and then in x = 2 ends 4 to the right$

Here P(1, 1) is reflected in x = 0 to (-1, 1), then in x = 2 to P'(5, 1). The mirrors are 2 apart and P has moved 4 to the right: one translation by ⟨4, 0⟩ does the same job. Two mirrors that cross at right angles make a half turn about the crossing point instead.

The board counts your moves and shows the fewest that land the shape. Any route that lands is right; the best route also teaches you which single move it was.

Challenge

The dashed target is where triangle ABC lands after a reflection in y = 1 and then a reflection in y = 4. Put ABC on the target in as few moves as you can, then press Check.

Try it yourself

$Move the shape onto its target$

Move the shape onto its target

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Transformations & Constructions

1Translations

Sliding a Shape Draw the Image Image Coordinates The Translation Rule Recap: Translations

4Combining Moves

One Move, Then Another Order MattersTwo MirrorsName the Move Recap: Combining Moves

7Drawing on Squared Paper

Lengths by Pythagoras Perpendicular Steps Squares by Area Right Triangles by Area Midpoints on the Grid Recap: Squared Paper

10Perpendiculars and Parallels

Perpendicular From a Point Perpendicular at a Point Parallel Through a Point Tools You Have Earned Recap: Parallels