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The Two Axes

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 6 of 60.

The y-axis is the upright line $x = 0$ . Reflecting in the y-axis changes the sign of x and keeps y: $(x,\ y) \to (-x,\ y)$ . The point crosses from right to left.

The x-axis is the level line $y = 0$ . Reflecting in the x-axis changes the sign of y instead: $(x,\ y) \to (x,\ -y)$ . D(2, 3) goes to D'(2, -3).

$Triangle DEF reflected in the x-axis$

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

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 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