﻿?> Rotation Worksheet | Problems & Solutions

# Rotation Worksheet

Rotation Worksheet
• Page 1
1.
Identify the incorrect statement.
I. A rotation is a transformation that turns a figure about a fixed point.
II. A rotation is an isometry.
III. A rotation does not change orientation.
IV. A figure has rotational symmetry, if the image after a rotation of 90° or less exactly fits on the original figure.
 a. III b. IV c. II d. I

#### Solution:

According to the definition of rotation, it is a transformation that turns the figure about a fixed point.

Rotaion is an isometry.

A rotation does not change orientation.

A figure has rotational symmetry if the image after a rotation of 180° or less exactly fits on the original figure.
[Definition of rotational symmetry.]

So, statement IV is incorrect.

2.
Rotate the given figure, 210° about the point P.

 a. Figure 3 b. Figure 1 c. Figure 2 d. Figure 4

#### Solution:

A type of transformation or movement that results when a geometric figure is turned about a fixed point is called rotation.

Draw a line from A to P.

Use protractor to measure 210° angle with side AP in counter clockwise direction.

Figure 2 makes an angles of 210° with the line AP.

Therefore Figure 2 is the correct answer.

3.
Recognise the figure which has rotational symmetry with an angle of rotation as 120°.

 a. Figure 2 b. Figure 4 c. Figure 1 d. Figure 3

#### Solution:

A figure has rotational symmetry if there is a rotation of 180° or less that maps the figure onto itself.

The angle of rotation is 360°n, where n is the number of times the figure repeats.

There are 8 spokes in figure 1. So the angle of rotation is 360 / 8 = 45°.

The angle of rotation for figure 2 is 360 / 4 = 90°.

The angle of rotation for figure 3 is 360 / 3 = 120°.

The angle of rotation for figure 4 is 360 / 5 = 72°.

So, the figure with an angle of rotation of 120° is Figure 3 only.

4.
Identify the center of rotation of the following figure.

 a. Figure 3 b. Figure 4 c. Figure 1 d. Figure 2

#### Solution:

Center of rotation is the point around which the figure is turned.

For the given figure, the center of rotation is the center of the figure.

The center of rotation is shown in figure 1.

5.
Identify the figure which has no rotational symmetry.

 a. Figure 3 b. Figure 4 c. Figure 2 d. Figure 1

#### Solution:

If you can rotate (or turn) a figure around a center point by 180° or less and the figure appears unchanged, then the figure has rotation symmetry.

Figures 1, 2 and 3 has rotational symmetry as the image maps itself if the figure is turned by 180° or less.

Figure 4 does not have rotational symmetry as it cannot map itself when it is turned to 180° or less.

6.
Rotate the given figure, 180° about P.

 a. Figure 3 b. Figure 4 c. Figure 2 d. Figure 1

#### Solution:

A type of transformation or movement, that results when a geometric figure is turned about a fixed point is called rotation.

Use protractor to measure 180° angle with side PQ in counter clockwise direction.

Figure 2 makes an angles of 180° with the actual figure.

7.
Mark and Dennis are playing ferris wheel which is rotating counter clockwise. If they are at the point marked 2, then what is the angle of rotation to reach the point marked 4?

 a. 100° b. 90° c. 75° d. 120°

#### Solution:

Place protractor on the line extending from center of the wheel to the point marked 2.

Measure the angle between point marked 2 and point marked 4 extended from the center of the wheel.

The angle is 120°.

8.
Select the rotational image of the given figure after a rotation of 300° in counter clockwise.

 a. Figure 4 b. Figure 1 c. Figure 3 d. Figure 2

#### Solution:

Place protractor on the line extending from centre to A.

Identify the figure that is turned 300°.

The figure which is rotated 300° in couter clockwise is Figure 3.

9.
Which of the following figures is not the rotational image?

 a. Figure 4 b. Figure 3 c. Figure 1 d. Figure 2

#### Solution:

Figures 1, 2 and 3 are the images obtained by rotating the actual figure.

Figure 4 is not the rotational image.
[Rotation does not change orientation.]

10.
Identify the figure which has rotational symmetry.

 a. Figure 2 b. Figure 3 c. Figure 4 d. Figure 1

#### Solution:

A type of transformation or movement, that results when a geometric figure is turned about a fixed point is called rotation.

If you can rotate (or turn) a figure around a center point by 180° or less and the figure appears unchanged, then the figure has rotation symmetry.

Figure 3 has rotational symmetry.