Question

find the image of b for a counterclockwise rotation of 240° about its center. a. point b b. point c c. point a

Explanation:

To solve this, we assume the figure is a regular triangle (since a 240° rotation in a triangle context makes sense, as 360°/3 = 120° per rotation between vertices). A counterclockwise rotation of 240° is equivalent to two 120° rotations (240° = 2×120°).

• A 120° counterclockwise rotation of point B would take it to point C.
• A second 120° counterclockwise rotation (total 240°) would take point C to point A.

Wait, no—wait, maybe it's a circle with three points A, B, C equally spaced (120° apart). So a counterclockwise rotation of 240° from B: each 120° moves to the next point. 240° is two steps. If B to C is 120°, C to A is another 120°, so total 240° from B counterclockwise is A? Wait, no—wait, maybe the center is the center of a regular triangle or a circle with three points. Let's think again.

Wait, maybe the figure is an equilateral triangle with center, and points A, B, C on the circumference, each 120° apart. So rotating B 240° counterclockwise: 240° is the same as -120° (since 360-240=120), but counterclockwise 240°: each 120° rotation moves to the next point. So from B, 120° CCW is C, 240° CCW is A? Wait, no—wait, if the points are A, B, C in clockwise order, then CCW 120° from B is A? Wait, maybe I got the direction wrong.

Alternatively, maybe the figure is a circle with three points, and the central angle between each pair is 120°. So rotating point B 240° counterclockwise: the image of B after 240° CCW rotation. Let's calculate the angle: 240° divided by 120° (the angle between each point) is 2. So moving 2 positions counterclockwise from B. If the order is B, C, A (CCW), then B to C is 120°, C to A is another 120°, so 240° from B CCW is A? Wait, but maybe the correct answer is A? Wait, no—wait, maybe the options are different. Wait, the options are A: point B, B: point C, C: point A.

Wait, maybe the figure is a regular triangle, and the center is the centroid. A 240° counterclockwise rotation: 360° - 240° = 120°, so a 240° CCW rotation is equivalent to a 120° clockwise rotation. Wait, no—rotation direction: counterclockwise is positive. So 240° CCW. If the triangle has vertices A, B, C in CCW order, then rotating B 240° CCW: each vertex is 120° apart. So from B, moving 240° CCW: 240° / 120° = 2 steps. So B -> C (120°), C -> A (240°). So the image of B after 240° CCW rotation is A. So the answer is C. point A.

Assuming the figure (e.g., a regular triangle or circle with three equally - spaced points A, B, C, 120° apart between adjacent points). A counter - clockwise rotation of 240° is equivalent to moving 2 steps of 120° each. Starting from point B, moving 120° counter - clockwise reaches point C, and moving another 120° (total 240°) reaches point A.

Answer:

C. point A