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Find the Mirror

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 9 of 61.

When you see a shape and its mirror image, you can find the mirror from any one corner. The mirror is the line through the midpoint of a point and its image, at right angles to the segment that joins them.

$Triangle PQR and its mirror image, with the mirror x = 2 between them$

Here P(5, 1) and P'(-1, 1) are level, so the segment between them is level and the mirror is upright. The midpoint is (2, 1), so the mirror is x = 2. Check it on a second corner: Q(5, 4) is 3 right of x = 2 and Q'(-1, 4) is 3 left of it.

The same method works for a slanted mirror: find the midpoint first, then the direction at right angles to the segment.

Challenge

Triangle ABC has been reflected onto the dashed target. Which move does it? Pick it, 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 Matters Two Mirrors Name 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

2Reflections

Reflecting in a Line The Two Axes The Line y = xFind the MirrorRecap: Reflections

5Dilations

Scaling From a Center Shrinking a Shape Dilating About a Point Negative Scale Factors Recap: Dilations

8Compass and Straightedge

Circles Keep Distances Why the Sides Match Angles You Built A 60° Angle Recap: Equilateral Triangle

11Constructed Shapes

A Square on a Segment The Regular Hexagon Copy an Angle A Tangent From a Point Recap: Constructed Shapes