Question

Math

Posted 6 months ago

```
Quadrilateral $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ is the image of quadrilateral $A B C D$ under a rotation about point $Q$.
Determine the angle of rotation.
Choose 1 answer:
(A) $-150^{\circ}$
(B) $-105^{\circ}$
(C) $105^{\circ}$
(D) $150^{\circ}$
```

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Answer from Sia

Posted 6 months ago

Solution by Steps

step 2

By examining the orientation of the two quadrilaterals, we can trace the path of one point to its new position after rotation

step 3

The angle of rotation is the measure of the angle formed at point $Q$ between the lines connecting $Q$ to a point on $ABCD$ and its corresponding point on $A'B'C'D'$

step 4

Using the given answer choices, we can eliminate the negative angles if the rotation is counterclockwise or the positive angles if the rotation is clockwise

step 5

The correct angle of rotation is the one that aligns all points of $ABCD$ with their corresponding points on $A'B'C'D'$ when applied

C

Key Concept

Angle of Rotation

Explanation

The angle of rotation is the angle through which a figure is rotated about a fixed point to reach its new position.

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