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Rotations of 90°, 180°, 270° and 360° About the Origin (Mathematics Lesson)

Common Rotations

A rotation can be by any angle about any center of rotation.

However, it can be time consuming to rotate a shape and even more difficult to describe a rotation.

Rotations of 90°, 180°, 270° and 360° about the origin, however, are relatively simple.

A Rotation of 90° About the Origin

The shape below has been rotated 90° (one quarter turn) clockwise about the origin:



Read more about a 90° rotation about the origin

A Rotation of 180° About the Origin

The shape below has been rotated 180° (one half turn) clockwise about the origin:



Read more about a 180° rotation about the origin

A Rotation of 270° About the Origin

The shape below has been rotated 270° (three quarter turns) clockwise about the origin:



Read more about a 270° rotation about the origin

A Rotation of 360° About the Origin

The shape below has been rotated 360° (one whole turn) clockwise about the origin:



Read more about a 360° rotation about the origin
Curriculum
Geometry Lessons
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Top Tip

HOW TO THINK OF ROTATIONS 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 in a series of one... two... three... four quarter turns, the rotations described on this page can be found.



Note
WHAT IS A ROTATION?

A rotation turns a shape around a center.

A rotation is a type of transformation.

CLOCKWISE AND COUNTER-CLOCKWISE

The direction of rotation is needed to describe a rotation.

  • If the rotation is in the same direction as the hands of a clock, the direction is clockwise.


  • If the rotation is in the opposite direction as the hands of a clock, the direction is counter-clockwise or anti-clockwise.


  • A ROTATION CAN BE DESCRIBED AS BOTH CLOCKWISE AND COUNTER-CLOCKWISE

    Any rotation can be described as both clockwise and clockwise.

    The rotation below can be described as both 90° clockwise and 270° counter-clockwise:



    If a rotation is θ clockwise, it is 360 - θ counter-clockwise.