Final answer:
The question involves finding the coordinates of a point after a 240-degree rotation around a circle with a diameter of 22 cm, using geometry and vector operations. It includes calculating the position using trigonometric functions of the rotation angle applied to the radius of the circle.
Step-by-step explanation:
The problem at hand falls under the category of Mathematics, more specifically, it is related to geometry and vector operations. The student is given a scenario where a point on a circle with a diameter of 22 cm is rotated by 240 degrees. The objective is to find the new coordinates of that point after rotation, assuming the original point is at the center of the circle. The correct answer should be deduced by applying rotational transformation rules in a two-dimensional plane.
To find the new coordinates after a 240-degree rotation, we first note that the radius of the circle would be 11 cm (half the diameter). Point B initially at (0,0) - the circle's center - will move along the circumference after the rotation. A rotation of 240 degrees is equivalent to a rotation of 240 - 360 = -120 degrees in standard position (counterclockwise from the positive x-axis). After rotating point B, the coordinates can be obtained using the formulas Bx = r * cos(theta) and By = r * sin(theta), where theta is the angle of rotation and r is the radius of the circle.
Applying these formulas, we have:
Performing these calculations will yield the new coordinates of point B, which can be matched with the given options.