HiSET: Math : Rotations

Study concepts, example questions & explanations for HiSET: Math

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Example Questions

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Example Question #1 : Rotations

What is the result of rotating the point  about the origin in the plane by ?

Possible Answers:

Correct answer:

Explanation:

Rotating a point 

geometrically in the plane about the origin  is equivalent to negating the coordinates of the point algebraically to obtain

.

Thus, since our initial point was

we negate both coordinates to get

as the rotation about the origin by .

Example Question #2 : Rotations

Nonagons

Examine the figures in the above diagram. Figure 2 is the result of performing which of the following transformations on Figure 1?

Possible Answers:

Correct answer:

Explanation:

The diagram below superimposes the two figures:

Nonagons

The transformation moves the black diagonal to the position of the red diagonal, and, consequently, points  and  to points  and , respectively. This constitutes two-tenths of a complete turn clockwise, or a clockwise rotation of 

Example Question #3 : Rotations

Question mark

Rotate the above figure  counterclockwise. Which figure is the result?

Possible Answers:

Question mark

None of the other choices gives the correct result.

Question mark

Question mark

Question mark

Correct answer:

Question mark

Explanation:

A counterclockwise rotation of  is  ofa complete rotation. Observe the following diagram:

Question mark

In the right figure, the question mark has been turned one-eighth of a complete turn counterclockwise. This is the correct orientation.

Example Question #118 : Hi Set: High School Equivalency Test: Math

Hexagon

Let  and  be the midpoints of  and , respectively.

Rotate the above hexagon  clockwise, then reflect it about the line through . Call  the image of  after these transformations.

 will be located in the same position as which of the following points?

Possible Answers:

Correct answer:

Explanation:

 rotation is equivalent to  of a complete rotation, so rotate as follows:

Hexagon

The image of  under this rotation, which we will call , is at .

Now, locate the midpoints  and , and construct the line  as described and shown below. Perform the reflection:

Hexagon

It can be seen that the image of  under this transformation - the desired  - is located at .

Example Question #4 : Rotations

Octagon

In the above octagon, let  and  be the midpoints of  and , respectively.

Rotate the above octagon  counterclockwise, then reflect it about  . Call  the image of  after these transformations.

 will be located in the same position as which of the following points?

Possible Answers:

Correct answer:

Explanation:

 rotation is equivalent to  of a complete rotation, so rotate as follows:

Octagon

The image of  under this rotation, which we will call , is at .

Now, locate the midpoints  and , and construct the line  as described and shown below. Perform the reflection:

Octagon

The image of  under this transformation - the desired  - is located at .

Example Question #5 : Rotations

Hexagon

Rotate the above hexagon  counterclockwise, then reflect it about . Call  the image of  after these transformations.

 will be located in the same position as which of the following points?

Possible Answers:

Correct answer:

Explanation:

 rotation is equivalent to  of a complete rotation, so rotate as follows:

Hexagon

The image of  under this rotation, which we will call , is at .

Now, construct , and reflect the hexagon about this line:

Hexagon

The image of  under this reflection - the desired  - is located at  itself.

 

Example Question #6 : Rotations

Between 6:15 and 6:40, the minute hand of a clock undergoes which of the following clockwise rotations?

Possible Answers:

Correct answer:

Explanation:

Between 6:15 and 6:40,

minutes elapse.

The minute hand of a clock rotates one complete clockwise turn about its mount over the course of 60 minutes. Therefore, over 25 minutes, the minute hand rotates clockwise.

Example Question #7 : Rotations

Over the course of 20 minutes, the hour hand of a clock undergoes which of the following rotations?

Possible Answers:

Correct answer:

Explanation:

The hour hand of a clock makes one complete  clockwise rotation over the course of 12 hours, or

minutes.

Therefore, over the course of 20 minutes, the hour hand rotates

.

Example Question #8 : Rotations

Over the course of one minute and forty seconds, the minute hand of a clock undergoes which of the following clockwise rotations?

Possible Answers:

Correct answer:

Explanation:

The minute hand of a clock rotates one complete clockwise turn about its mount over the course of 60 minutes, or, equivalently, since there are 60 seconds in a minute, every

seconds.

Over the course of 1 minute 40 seconds - or, since one minute is equal to 60 seconds,  seconds - the minute hand rotates clockwise

.

Example Question #9 : Rotations

Letters

Examine the figures in the above diagram. The figure at right is the result of performing which of the following transformations on the figure at left?

Possible Answers:

 counterclockwise rotation

 clockwise rotation

 counterclockwise rotation

 rotation

 clockwise rotation

Correct answer:

 clockwise rotation

Explanation:

Examine the figure below:

1

If we connect the horizontal line with the line along the rotated nine at right, we see that it is the result of a one-third turn clockwise; the angle between them 

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