Final Answer:
The length of line segment c'd' after rotating rectangle abcd 90° clockwise about the origin remains the same as the length of side ab, given that the rotation is about the origin.
Step-by-step explanation:
When a point is rotated 90° clockwise about the origin in a coordinate plane, its new coordinates (x', y') can be determined by swapping the x and y coordinates and changing the sign of the new x-coordinate. Applying this to the rectangle, the side cd would become parallel to the x-axis, and after rotating 90° clockwise, it will coincide with side ab. Therefore, the length of line segment c'd' is the same as the length of side ab, maintaining its measure in units.
This property holds true because rotating a shape about the origin involves changing its orientation in space but doesn't alter the actual dimensions or lengths of its sides. The transformation simply changes the position of the points, preserving the lengths and angles within the shape. Thus, after rotating the rectangle 90° clockwise, the length of c'd' remains identical to the length of ab.
In summary, when rotating a shape, in this case, a rectangle, 90° clockwise about the origin in a coordinate plane, the length of the line segment c'd' will be equivalent to the length of side ab, retaining its measure in units due to the property of rotation preserving side lengths.