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The Half Turn

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 12 of 61.

A half turn is a rotation by 180°. Turning halfway round, clockwise or counterclockwise, ends in the same place, so a half turn needs no direction.

$Triangle PQR and its image after a half turn about the origin$

About the origin, a half turn sends (x, y) to (-x, -y): the step from O to the point is reversed. P(3, -1) goes to P'(-3, 1). The center is the midpoint of P and P', and of every other point and its image. That gives a way to find the center of any half turn: take the midpoint of one corner and its image.

Challenge

Draw the image of triangle ABC after a half turn about the origin. Drag A', B' and C' into place, 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

3Rotations

Turning About a PointThe Half TurnQuarter-Turn Rules A Center Off the Origin Recap: Rotations

6Symmetry

Lines of Symmetry Rotational Symmetry Regular Polygons Symmetry Is a Move Recap: Symmetry

9Bisectors

The Perpendicular Bisector The Midpoint Bisecting an Angle Half of 60°Recap: Bisectors

12Final Challenges

Final: Footprints Final: Two Moves, One Rule Final: Mirror on the Grid Final: The Fair Well Final: The Tangent Road