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Turning About a Point

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 10 of 60.

A rotation turns a shape about a fixed point, the center. Every point keeps its distance from the center and turns through the same angle. By convention a positive angle turns counterclockwise.

$Triangle PQR turned a quarter turn clockwise about the origin$

Here PQR turns 90° clockwise about the origin O. P(3, 1) is 3 right and 1 up from O; after a quarter turn clockwise that step becomes 1 right and 3 down, so P' is (1, -3). The image keeps its size and shape and is not flipped: the corners still go round in the same order.

On the board, the move is Rotate: choose 90°, 180° or 270°, the direction and the center (the origin unless you change it), then press Apply.

Challenge

Turn triangle ABC about the origin onto the dashed target: choose the angle and the direction, press Apply, 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

3Rotations

Turning About a PointThe Half Turn Quarter-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