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The Two Axes

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 7 of 61.

The two axes are the mirrors you meet most. Reflecting in the x-axis (the line y = 0) keeps every x and changes the sign of every y: (x, y) → (x, -y). A point 3 above the axis ends up 3 below it.

$Triangle DEF reflected in the x-axis$

In the figure D(2, 3) goes to D'(2, -3) and F(2, 1) to F'(2, -1): the x-coordinates stay, the y-coordinates swap sign. Reflecting in the y-axis (the line x = 0) is the same idea turned on its side. Now y stays and x changes sign: (x, y) → (-x, y).

Challenge

Triangle ABC is reflected in the y-axis (the line x = 0). Write the coordinates of A', B' and C', 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 LineThe Two AxesThe Line y = x Find the Mirror Recap: 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