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Rotating a Shape

(KS2, Year 6)

Rotating a Shape

A shape can be rotated. When a shape is rotated, each point on the shape is turned by an angle about a centre of rotation.

How to Rotate a Shape

Rotating a shape is easy.

Question

Rotate the shape below by 60° clockwise about the point (3, 1). rotate a shape example

Step-by-Step:

1

Plot the centre of rotation. In our example, the Cartesian coordinates of the centre of rotation is (3, 1). It is 3 units along the x-axis and 1 unit up the y-axis. rotate_a_shape_example_step_1
Each point on the shape is rotated by the same amount. Let us choose a point on the shape and rotate it. We will rotate point A.

2

Draw a line from the centre of rotation to point A. rotate_a_shape_step_2

3

Measure the length of this line. rotate_a_shape_step_3

4

Measure the angle of rotation (60°) from the line. Using a protractor, find 60° clockwise from the line found. Mark this angle. rotate_a_shape_step_4

5

Draw a line from the centre of rotation. It must be the same length as the line in Step 3 and be at the angle found in Step 4. rotate_a_shape_step_5
Point A has been rotated 60° about (3, 1) to find A', the corresponding point on the rotated shape.rotate_a_shape_point_A_answerRepeat for points B and C:rotate_a_shape_example_A_B_C

Answer:

With all the vertices (corners) of the shape rotated, the rotated shape can be drawn:

rotate a shape answer

Lesson Slides

The slider below shows another real example of how to rotate a shape.
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This page was written by Stephen Clarke.

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

    counter-clockwise_mini

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:

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