All HiSET: Math Resources
Example Questions
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?
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 #2 : 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 #3 : Rotations
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 #123 : Hi Set: High School Equivalency Test: Math
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 counterclockwise rotation
A clockwise rotation
A counterclockwise rotation
A 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
Example Question #21 : Understand Transformations In The Plane
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 counterclockwise rotation
A clockwise rotation
A clockwise rotation
None of the other choices gives the correct response.
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-eighth turn clockwise; the angle between them .
Example Question #22 : Understand Transformations In The Plane
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 counterclockwise rotation
A counterclockwise rotation
A clockwise rotation
A clockwise rotation
A rotation
A counterclockwise rotation
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
.
Example Question #23 : Understand Transformations In The Plane
Over the course of one hour and twenty minutes, the hour hand of a clock undergoes which of the following clockwise rotations?
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
.
Example Question #1 : Dilations
On the above right triangle perform a dilation of scale factor with the center of the dilation at the circumcenter of the triangle. Let the images of
,
, and
be
,
, and
, respectively.
Which of the following correctly shows relative to
?
The circumcenter of a triangle can be located by finding the intersection of the perpendicular bisectors of the three sides of the triangle. The perpendicular bisectors are shown below, with point of intersection :
It can be seen that, as is characteristic of a right triangle, this point is the midpoint of the hypotenuse. Construct . A dilation of scale factor
with center
can be performed by letting
,
, and
be the midpoints of
,
, and
, respectively:
Removing the perpendicular bisectors and , we see that the correct choice is the figure
Example Question #2 : Dilations
On the above right triangle perform a dilation of scale factor with the center of the dilation at the centroid of the triangle. Let the images of
,
, and
be
,
, and
, respectively.
Which of the following correctly shows relative to
?
The centroid of a triangle can be located by finding the intersection of the three medians of the triangle - the segments that connect each vertex to the midpoint of its opposite side. The medians are shown below, with point of intersection :
A dilation of scale factor with center
can be performed by letting
,
, and
be the midpoints of
,
, and
, respectively:
Removing the medians and , we see that the correct choice is the figure
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