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 #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 #2 : 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 #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 counterclockwise rotation
A clockwise rotation
A counterclockwise rotation
A clockwise 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 #61 : Measurement And Geometry
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 clockwise rotation
A counterclockwise 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 #11 : 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 counterclockwise rotation
A rotation
A clockwise 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 #13 : Rotations
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 #1 : 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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