Rotations - HiSET
Card 1 of 52
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?
Rotate the above hexagon 
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A 
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, construct 
, and reflect the hexagon about this line:
The image of 
under this reflection - the desired 
- is located at 
itself.
A 
The image of 
Now, construct 
The image of 
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What is the result of rotating the point 
about the origin in the plane by 
?
What is the result of rotating the point
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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 
.
Rotating a point
geometrically in the plane about the origin
Thus, since our initial point was
we negate both coordinates to get
as the rotation about the origin by
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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?
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?
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Examine the figure below.
If we connect the horizontal line with the line along the rotated "omega" at right, we see that it is the result of a one-sixth turn counterclockwise; the angle between them is one sixth of 
, or 
.
Examine the figure below.
If we connect the horizontal line with the line along the rotated "omega" at right, we see that it is the result of a one-sixth turn counterclockwise; the angle between them is one sixth of 
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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?
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?
Tap to reveal answer
Examine the figure below:
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 
Examine the figure below:
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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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?
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?
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Examine the figure below:
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-eighth turn clockwise; the angle between them 
.
Examine the figure below:
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-eighth turn clockwise; the angle between them 
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Examine the figures in the above diagram. Figure 2 is the result of performing which of the following transformations on Figure 1?
Examine the figures in the above diagram. Figure 2 is the result of performing which of the following transformations on Figure 1?
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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 
The diagram below superimposes the two figures:
The transformation moves the black diagonal to the position of the red diagonal, and, consequently, points 
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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?
Let 
Rotate the above hexagon 
Tap to reveal answer
A 
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 
.
A 
The image of 
Now, locate the midpoints 
It can be seen that the image of 
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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?
In the above octagon, let 
Rotate the above octagon 
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A 
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 
.
A
The image of 
Now, locate the midpoints
The image of 
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Rotate the above figure 
counterclockwise. Which figure is the result?
Rotate the above figure 
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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.
A counterclockwise rotation of 
In the right figure, the question mark has been turned one-eighth of a complete turn counterclockwise. This is the correct orientation.
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Over the course of 20 minutes, the hour hand of a clock undergoes which of the following rotations?
Over the course of 20 minutes, the hour hand of a clock undergoes which of the following rotations?
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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
.
The hour hand of a clock makes one complete 
minutes.
Therefore, over the course of 20 minutes, the hour hand rotates
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Over the course of one minute and forty seconds, the minute hand of a clock undergoes which of the following clockwise rotations?
Over the course of one minute and forty seconds, the minute hand of a clock undergoes which of the following clockwise rotations?
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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
.
The minute hand of a clock rotates one complete
Over the course of 1 minute 40 seconds - or, since one minute is equal to 60 seconds, 
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Over the course of one hour and twenty minutes, the hour hand of a clock undergoes which of the following clockwise rotations?
Over the course of one hour and twenty minutes, the hour hand of a clock undergoes which of the following clockwise rotations?
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The hour hand of a clock makes one complete clockwise rotation over the course of 12 hours, or, since one hour is equal to 60 minutes,
Therefore, over the course of 1 hour 20 minutes - which is equal to 
minutes - the hour hand rotates
.
The hour hand of a clock makes one complete
Therefore, over the course of 1 hour 20 minutes - which is equal to 
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Between 6:15 and 6:40, the minute hand of a clock undergoes which of the following clockwise rotations?
Between 6:15 and 6:40, the minute hand of a clock undergoes which of the following clockwise rotations?
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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.
Between 6:15 and 6:40,
minutes elapse.
The minute hand of a clock rotates one complete 
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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?
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?
Tap to reveal answer
Examine the figure below:
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-eighth turn clockwise; the angle between them .
Examine the figure below:
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-eighth turn clockwise; the angle between them
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Over the course of 20 minutes, the hour hand of a clock undergoes which of the following rotations?
Over the course of 20 minutes, the hour hand of a clock undergoes which of the following rotations?
Tap to reveal answer
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
.
The hour hand of a clock makes one complete
minutes.
Therefore, over the course of 20 minutes, the hour hand rotates
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What is the result of rotating the point about the origin in the plane by ?
What is the result of rotating the point
Tap to reveal answer
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 .
Rotating a point
geometrically in the plane about the origin
Thus, since our initial point was
we negate both coordinates to get
as the rotation about the origin by
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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?
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?
Tap to reveal answer
Examine the figure below.
If we connect the horizontal line with the line along the rotated "omega" at right, we see that it is the result of a one-sixth turn counterclockwise; the angle between them is one sixth of , or .
Examine the figure below.
If we connect the horizontal line with the line along the rotated "omega" at right, we see that it is the result of a one-sixth turn counterclockwise; the angle between them is one sixth of
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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?
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?
Tap to reveal answer
Examine the figure below:
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
Examine the figure below:
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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Examine the figures in the above diagram. Figure 2 is the result of performing which of the following transformations on Figure 1?
Examine the figures in the above diagram. Figure 2 is the result of performing which of the following transformations on Figure 1?
Tap to reveal answer
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
The diagram below superimposes the two figures:
The transformation moves the black diagonal to the position of the red diagonal, and, consequently, points
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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?
Let
Rotate the above hexagon
Tap to reveal answer
A 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 .
A
The image of
Now, locate the midpoints
It can be seen that the image of
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