Find the Mirror

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 8 of 60.

Swapping the coordinates flipped the triangle over the slanted line $y = x$ . So it was a reflection. You can find any mirror line from one point and its image, in three steps.

Join a point to its image with a segment.
Mark the midpoint, the point halfway along that segment.
The mirror goes through the midpoint, at a right angle to the segment.

P(5, 1) and P'(-1, 1) are level with each other, so the mirror is upright. It goes through their midpoint (2, 1), so it is $x = 2$ .

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

Challenge

Triangle ABC has been reflected onto the dashed target. Which move does this? Pick it.

Then press Check.

Try it yourself

$Move the shape onto its target$

Move the shape onto its target

All lessons in Transformations & Constructions

1Translations

Sliding a Shape Draw the Image 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