HiSET: Math : Dilations

Study concepts, example questions & explanations for HiSET: Math

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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.

Possible Answers:

None of the other choices gives the correct response.

Correct answer:

Explanation:

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:

1

 

Substituting in the circle formula, this is 

,

or

.

Example Question #12 : Dilations

Obtuse triangle

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  ?

Possible Answers:

Obtuse triangle

Obtuse triangle

Obtuse triangle

Obtuse triangle

1

Correct answer:

Obtuse triangle

Explanation:

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  :

Obtuse triangle

Construct , and . A dilation of scale factor   with center  can be performed by letting , and  be the midpoints of , and , respectively: 

Obtuse triangle

Removing the perpendicular bisectors and , we see that the correct choice is the figure

Obtuse triangle

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