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HiSET: Math : Rotations

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Example Questions

Example Question #123 : Hi Set: High School Equivalency Test: Math

Letters

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?

Possible Answers:

A $90^{\circ }$ $\displaystyle 90^{\circ }$ counterclockwise rotation

A $45^{\circ }$ $\displaystyle 45^{\circ }$ clockwise rotation

None of the other choices gives the correct response.

A $90^{\circ }$ $\displaystyle 90^{\circ }$ clockwise rotation

A $45^{\circ }$ $\displaystyle 45^{\circ }$ counterclockwise rotation

Correct answer:

A $45^{\circ }$ $\displaystyle 45^{\circ }$ clockwise rotation

Explanation:

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 $\frac{1}{8} \times 360^{\circ } = 45^{\circ }$ $\displaystyle \frac{1}{8} \times 360^{\circ } = 45^{\circ }$.

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Example Question #21 : Understand Transformations In The Plane

Letters

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?

Possible Answers:

A $120^{\circ }$ $\displaystyle 120^{\circ }$ counterclockwise rotation

A $120^{\circ }$ $\displaystyle 120^{\circ }$ clockwise rotation

A $60^{\circ }$ $\displaystyle 60^{\circ }$ clockwise rotation

A $60^{\circ }$ $\displaystyle 60^{\circ }$ counterclockwise rotation

A $180^{\circ }$ $\displaystyle 180^{\circ }$ rotation

Correct answer:

A $60^{\circ }$ $\displaystyle 60^{\circ }$ counterclockwise rotation

Explanation:

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 $360^{\circ }$ $\displaystyle 360^{\circ }$, or $\frac{1}{6} \times 360^{\circ } = 60^{\circ }$ $\displaystyle \frac{1}{6} \times 360^{\circ } = 60^{\circ }$.

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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?

Possible Answers:

$20 ^{\circ }$ $\displaystyle 20 ^{\circ }$

$30^{\circ }$ $\displaystyle 30^{\circ }$

$10^{\circ }$ $\displaystyle 10^{\circ }$

$40 ^{\circ }$ $\displaystyle 40 ^{\circ }$

$60^{\circ }$ $\displaystyle 60^{\circ }$

Correct answer:

$40 ^{\circ }$ $\displaystyle 40 ^{\circ }$

Explanation:

The hour hand of a clock makes one complete $360^{\circ }$ $\displaystyle 360^{\circ }$ clockwise rotation over the course of 12 hours, or, since one hour is equal to 60 minutes,

$12 \times 60 = 720\textup{ minutes}$ $\displaystyle 12 \times 60 = 720\textup{ minutes}$

Therefore, over the course of 1 hour 20 minutes - which is equal to $1 \times 60 + 20 = 80$ $\displaystyle 1 \times 60 + 20 = 80$ minutes - the hour hand rotates

$\frac{80}{720} \times 360 ^{\circ } = 40^{\circ }$ $\displaystyle \frac{80}{720} \times 360 ^{\circ } = 40^{\circ }$.

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HiSET: Math : Rotations

Study concepts, example questions & explanations for HiSET: Math

All HiSET: Math Resources

Example Questions

Example Question #123 : Hi Set: High School Equivalency Test: Math

Example Question #21 : Understand Transformations In The Plane

Example Question #23 : Understand Transformations In The Plane

All HiSET: Math Resources

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