Question

which of the following statements is true about rotation about the origin in terms of angles, circles, and line segments? select all that apply. the path of a point on the figure as it rotates is an arc centered at the origin. a rotation turns the figure about the origin by a given angle. rotating a point 180° creates a right angle through the original and final points with a vertex at the origin. a rotation of 90° turns the figure into a mirror image of the original. the distance between the point and the origin remains the same through the rotation.

Explanation:

1. When rotating a point about the origin, the distance from the point to the origin (radius) remains constant. The path of the point is an arc centered at the origin.
2. A 90 - degree rotation does not create a mirror - image. A reflection creates a mirror - image.
3. Rotating a point 180 degrees creates a straight - line segment (a diameter of the circle of rotation) between the original and final points with the origin as the mid - point. A rotation turns the figure about the origin by a given angle.

Answer:

The path of a point on the figure as it rotates is an arc centered at the origin.
A rotation turns the figure about the origin by a given angle.
The distance between the point and the origin remains the same through the rotation.