# HiSET: Math : Rotations

## Example Questions

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### Example Question #51 : Measurement And Geometry

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

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 #11 : Understand Transformations In The Plane

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

Explanation:

The diagram below superimposes the two figures:

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 #1 : Rotations

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

None of the other choices gives the correct result.

Explanation:

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

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

### Example Question #1 : Rotations

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?

Explanation:

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

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:

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

### Example Question #1 : Rotations

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?

Explanation:

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

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:

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

### Example Question #1 : Rotations

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?

Explanation:

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

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

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

### Example Question #1 : Rotations

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

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 #1 : Rotations

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

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 #1 : Rotations

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

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 #2 : Rotations

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?

counterclockwise rotation

counterclockwise rotation

rotation

clockwise rotation

clockwise rotation