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) $150^{\circ}$

Question

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) $150^{\circ}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine the angle of rotation, we need to compare the positions of at least two corresponding points on quadrilaterals $ABCD$ and $A'B'C'D'$. ‖ ‖ 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.⚹◊What formula can be used to calculate the angle of rotation when rotating a quadrilateral around a point?⍭ Generate me a similar question◊

Sia