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A Rotation of 180° About the Origin (Mathematics Lesson)

A 180° Rotation About the Origin

A rotation is described by the angle the shape turns about a center of rotation.



The shape above has been rotated 180° clockwise (the angle of reflection) about the origin (0, 0) (the center of rotation).

Real Examples of a Rotation of 180° About the Origin

All of the following shapes have been rotated by 180° clockwise about the origin:





90°, 270° and 360° Rotations About the Origin

90°, 270° and 360° rotations about the origin are also commonly examined:

Read more about a 90° rotation about the origin
Read more about a 270° rotation about the origin
Read more about a 360° rotation about the origin
Curriculum
Geometry Lessons
Interactive Test
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Top Tip
180° IS A QUARTER TURN

180° is a half turn.



Note
WHAT IS A ROTATION?

A rotation turns a shape around a center.

A rotation is a type of transformation.

HOW TO THINK OF ROTATIONS OF 180° ABOUT THE ORIGIN

Imagine a shape is drawn on a pair of axes on a sheet of paper...



Imagine sticking a pin through the origin and into a surface.



If you span the paper around, the pin would stay in place and every other point on the paper would turn in a circle around it.

By turning the paper a half turn, a 180° rotation about the origin will take place.