All HiSET: Math Resources
Example Questions
Example Question #11 : Dilations
On the graph of the equation
,
perform a dilation with center and scale factor .
Give the equation of the resulting circle.
None of the other choices gives the correct response.
The graph of the equation
is a circle with center and radius .
,
or
is a circle with center at origin and radius 8.
A dilation of a circle with scale factor will result in multiplying that radius by , so the radius of the circle will be .
To find the center of the image, note that the origin is 4 units below . The center of the new circle must be units below , so this center will be , or . See the figure below:
Substituting in the circle formula, this is
,
or
.
Example Question #12 : Dilations
On the above obtuse 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 :
Construct , , and . 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
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