Solved Examples and Worksheet for Transformations-Rotations

Q1Rotate the given figure, 230° about the point P.


A. Figure 3
B. Figure 4
C. Figure 1
D. Figure 2

Solutions
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Step: 1
A type of transformation or movement that results when a geometric figure is turned about a fixed point is called rotation.
Step: 2
Draw a line from A to P.
Step: 3
Use protractor to measure 230° angle with side AP in counter clockwise direction.
Step: 4
Figure 3 makes an angles of 230° with the line AP.
Step: 5
Therefore Figure 3 is the correct answer.
Correct Answer is :   Figure 3
Q2Mark and Dennis are riding a Ferris wheel which is rotating counter clockwise. If they are at the point marked point marked 4, then what is the angle of rotation to reach the point marked 6 ?


A. 120°
B. 100°
C. 75°
D. 90°

Solutions
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Step: 1
Place protractor on the line extending from center of the wheel to the point marked 4.
Step: 2
Measure the angle between point marked 4 and point marked 6 extended from the center of the wheel.
Step: 3
The angle is 120°.
Correct Answer is :   120°
Q3Find the angle of rotation about C that maps figure 1 to figure 2.

A. 80°
B. 45°
C. 90°
D. 60°

Solutions
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Step: 1
Mark the points B and B'.
Step: 2
Join B to C and B' to C.
Step: 3
Measure the angle between the lines.
Step: 4
The angle is observed as 90°.
  [Use protractor.]
Correct Answer is :   90°
Q4Find the angle of rotation that maps number '6' to number '9'.

A. 180°
B. 90°
C. 120°
D. 75°

Solutions
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Step: 1
A type of transformation or movement that results when a geometric figure is turned about a fixed point
Step: 2
Turn the number 6 with respect to the point to get number 9.
Step: 3
Measure the angle between the numbers.
  [Use protractor.]
Step: 4
The number 6 should be turned to 180° to get number 9.
Correct Answer is :   180°
Q5The 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. 270°
C. 180°
D. 90°

Solutions
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Step: 1
A type of transformation or movement, that results when a geometric figure is turned about a fixed point is called rotation.
Step: 2
Measure the angle between ON and LOW in clockwise direction.
Step: 3
The angle between them is 90°.
Step: 4
The knob should be turned 90° to LOW the machine.
Correct Answer is :   90°
Q6Select the rotational image of a figure after a rotation of 45° counter clockwise.


A. Figure 4
B. Figure 3
C. Figure 1
D. Figure 2

Solutions
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Step: 1
A type of transformation or movement, that results when a geometric figure is turned about a fixed point is called rotation.
Step: 2
Use protractor to measure the angle of rotation.
Step: 3
Figure 2 is rotated to 45°.
Step: 4
So, Figure 2 is the answer.
Correct Answer is :   Figure 2
Q7Rotate the given figure 45° about point P in clockwise direction. Select the resulting figure.

A. Figure 4
B. Figure 2
C. Figure 3
D. Figure 1

Solutions
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Step: 1
A rotation is a transformation that turns the figure about a fixed point.
Step: 2
Using protractor measure the angle of rotation in clockwise direction.
Step: 3
Figure 1 is rotated to 45° about the point P
Step: 4
So, Figure 1 is the answer.
Correct Answer is :   Figure 1
Q8Identify the fihure that shows the given figure, rotated through 180° in anti -clockwise direction.

A. Figure 2
B. Figure 1
C. Figure 3
D. Figure 4

Solutions
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Step: 1
When we rotate the given figure through an angle of 180° we obtain figure 4.
Correct Answer is :   Figure 4
Q9Identify the graph that shows the figure in graph A, rotated through 180° in anti-clockwise direction around the origin.

A. Graph 2
B. Graph 4
C. Graph 1
D. Graph 3

Solutions
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Step: 1
When we rotate the given figure in anti-clockwise through an angle of 180° we obtain Graph 4.
Correct Answer is :   Graph 3

HighSchool Math