A rigid motion, also known as an isometry, is a transformation of the plane that preserves the distance between every pair of points. This means that after a rigid motion is performed, the shape, size, and orientation of the figures are unchanged except for their position. Let's consider each of the options provided:
A. Rotate 90° counterclockwise around the origin.
Rotating a figure 90 degrees counterclockwise around the origin means turning it around the center (origin) without changing the size or shape of the figure. This transformation maintains the distance between all points within the figure, and thus it is a rigid motion.
B. Dilate by a factor of 2.
Dilation by a factor of 2 means enlarging a figure so that all points on the figure move away from a central point (often the origin) by twice their original distance from that point. This changes the size of the figure, which means the distances between points are not preserved. Therefore, dilation is not a rigid motion.
C. Translate 5 units right.
Translation involves moving every point of a figure the same distance in the same direction. In this case, translating a figure 5 units to the right will not change angles, lengths, or the shape of the figure. The distances between points in the figure remain unchanged. So, translation is a rigid motion.
D. Reflect over the y-axis.
Reflecting a figure over the y-axis means flipping it across the vertical axis that runs through the origin. This is like looking at the figure in a mirror placed along the y-axis. The shape and size of the figure remain the same after reflection, so the distances between points are the same. Reflection is also a rigid motion.
Out of the four transformations, only option B, 'Dilate by a factor of 2,' is not a rigid motion because it changes the distances between points in the figure. Hence, the correct answer is:
B. Dilate by a factor of 2.
