All HiSET: Math Resources
Example Questions
Example Question #11 : Understand Transformations In The Plane
What is the result of rotating the point about the origin in the plane by
?
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 #1 : Rotations
Examine the figures in the above diagram. Figure 2 is the result of performing which of the following transformations on Figure 1?
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.
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 #61 : Measurement And Geometry
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?
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
.
Example Question #21 : Understand Transformations In The Plane
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?
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
.
Example Question #61 : Measurement And Geometry
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?
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.
Example Question #1 : Rotations
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,
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 #121 : Hi Set: High School Equivalency Test: Math
Over the course of 20 minutes, the hour hand of a clock undergoes which of the following rotations?
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?
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 #1 : 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?
A clockwise rotation
A rotation
A clockwise rotation
A counterclockwise rotation
A counterclockwise rotation
A clockwise rotation
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
All HiSET: Math Resources
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