Final answer:
After a 360° rotation, the coordinates of a point remain unchanged. After a translation, the coordinates of the point change. After a reflection across y = x, the measure of the angle remains the same.
Step-by-step explanation:
A rigid transformation on a coordinate plane is a transformation that changes the position of a figure without altering its shape or size. Let's take a closer look at the transformations of square ABCD and determine which characteristics or corresponding parts will not remain the same.
A. The perimeter of a square is the total distance around the square. Since a rigid transformation does not change the shape or size, the perimeter of square A'B'C'D' will remain the same.
B. A rotation of 360° counterclockwise about the origin will bring point A' back to its original position. Therefore, the coordinates of point A' will not change and will be the same as those of point A before the rotation.
C. A translation of (-3, 2) shifts all points in the preimage the same distance in the same direction. The coordinates of B' will be different after this transformation; they will not be the same as point B before the translation.
D. A reflection across the line y = x will change the coordinates of the points by interchanging their x and y values, but the measure of angle B' will be same as B because reflections preserve angles.
So, the characteristic that will not remain the same after its respective transformation is the coordinates of B' after a translation.