A____ is the same distance from each point of a figure and its image.
A. translation vector
B. center of rotation
C. rigid transformation
D. line of reflection
D. line of reflection
D. line of reflection
The correct answer is B. center of rotation.
To understand why the center of rotation is the same distance from each point of a figure and its image, let's first review what a center of rotation is. In geometry, a rotation is a transformation that moves every point of a figure in a circular path around a fixed point called the center of rotation.
When a figure is rotated around a center of rotation, each point on the figure moves along an arc with the same radius, which is the distance between the point and the center of rotation. Therefore, the distance from each point of the figure to the center of rotation remains the same after the rotation.
This is true for both the original figure and its image. An image is formed when a figure is transformed using a rotation, and the image retains the same size and shape as the original figure. So, if you consider any point on the original figure and its corresponding image after the rotation, the distance between each point and the center of rotation remains unchanged.
Hence, the center of rotation is the same distance from each point of a figure and its image.