Question

point q was rotated by $-150^circ$ (the center of rotation is indicated).
which point is the image of q?
choose 1 answer:
a $a$
b $b$
c $c$
d $d$

Explanation:

Step1: Understand Rotation Direction

A rotation of \(-150^\circ\) is equivalent to a clockwise rotation of \(150^\circ\) (since negative angles represent clockwise rotation in standard position).

Step2: Analyze Distances and Angles

The center of rotation is fixed. We need to check the angle between the line from the center to \(Q\) and the line from the center to each candidate point (A, B, C, D) and ensure the distance from the center to \(Q\) is equal to the distance from the center to its image.

• For a clockwise rotation of \(150^\circ\), we can visualize the angle between the position of \(Q\) and the position of its image.
• By checking the relative positions and angles (using the center as the vertex), we find that the point \(A\) is not at the correct angle, \(C\) and \(D\) are at angles that don't match \(150^\circ\) clockwise from \(Q\), but \(B\) is at the angle corresponding to a \(150^\circ\) clockwise rotation (or \(-150^\circ\) rotation) from \(Q\) with the same distance from the center.

Answer:

B. \( B \)