How to Rotate a Shape

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 center 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).

Step-by-Step:

1

Plot the center of rotation.

In our example, the Cartesian coordinates of the center of rotation is (3, 1). It is 3 units along the x-axis and 1 unit up the y-axis.

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 center of rotation to point A.

3

Measure the length of this line.

4

Measure the angle of rotation (60°) from the line.

Using a protractor, find 60° clockwise from the line found.

Mark this angle.

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.

Point A has been rotated 60° about (3, 1) to find A', the corresponding point on the rotated shape.

Repeat for points B and C:

Answer:

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

Slider

The slider below shows another real example of how to rotate a shape.

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See Also

What is geometry? What are transformations? What is an angle?