﻿ Rotation Worksheet - Page 2 | Problems & Solutions

# Rotation Worksheet - Page 2

Rotation Worksheet
• Page 2
11.
What is the angle of rotation about the point P that maps figure 1 to figure 2?

 a. 90° b. 15° c. 120° d. 45°

#### Solution:

A rotation is a transformation that turns the figure about a fixed point.

Mark point A and A'.

Join P to A and A' and measure the angle of rotation.
[Use protractor.]

The angle of rotation is observed as 45°.

12.
The following figures have rotational symmetry. Determine the angle of rotation for each of them.

 a. 60°, 72°, 60°, 90° b. 72°, 60°, 72°, 120° c. 60°, 42°, 42°, 120° d. 60°, 72°, 72°, 60°

#### 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 defined as the number of degrees that a figure is rotated about a fixed point.

The angle of rotation is 360° / n, where n is the number of times a figure is repeated.

The angle of rotation for figure 1 = 360° / 5 = 72°

The angle of rotation for figure 2 = 360° / 6 = 60°

The angle of rotation for figure 3 = 360° / 5 = 72°

The angle of rotation for figure 4 = 360° / 3 = 120°

So the angles are 72°, 60°, 72°, 120°

13.
Which of the following figures are not the rotational images of the given figure.

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

#### Solution:

A rotation is a transformation that turns the figure about a fixed point.

Figure 2 and 4 are the images resulting from rotation.

Figure 1 and 3 are not the rotational images.
[Rotation does not change orientation.]

14.
Recognise the center of rotation of the given figure.

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

15.
Which of the following is not the rotational image of the given figure?

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

#### Solution:

Figures 1, 2 and 3 are the rotational images.

Figure 3 is not the image obtained from the rotation of the figure shown.
[Rotation does not change orientation.]

16.
The knob indicates that the machine is 'ON'. What angle should the knob be turned to switch 'LOW' the machine. ( Turn in clockwise direction.)

 a. 180° b. 90° c. 270° d. 180°

#### Solution:

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

Measure the angle between ON and LOW in clockwise direction.

The angle between them is 90°.

The knob should be turned 90° to LOW the machine.

17.
Select the rotational image of a figure after a rotation of 315° counter clockwise.

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

#### 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 the angle of rotation.

Figure 4 is rotated to 315°.

So, Figure 4 is the answer.

18.
Does the following figure have rotational symmetry? If it has, give the angle of rotation.

 a. no b. yes, 90° c. yes, 180° d. yes, 60°

#### Solution:

A figure is said to have rotational symmetry, if the roation of 180° or less maps the figure onto itself.

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

The angle of rotation = 360° / 4= 90°

The figure shown has rotational symmetry as it maps itself if it is turned to 90°.

19.
Which of the following is the rotational image of the given figure?

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

#### Solution:

A rotation is a transformation that turns the figure about a fixed point.

Figures 1, 3 and 4 are not the rotational images of the given figure.
[Rotation does not change orientation.]

Figure 2 is the rotational image of the given figure.

20.
Rotate the given figure 45° about point P in clockwise direction. Select the resulting figure.

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

#### Solution:

A rotation is a transformation that turns the figure about a fixed point.

Using protractor measure the angle of rotation in clockwise direction.

Figure 1 is rotated to 45° about the point P

So, Figure 1 is the answer.