To determine the measure of angle B' after the square ABCD is rotated 90° clockwise about the origin, let's analyze the rotation.
When a point (x, y) is rotated 90° clockwise about the origin, the new coordinates become (y, -x). In the case of square ABCD, each vertex will undergo the same transformation.
Assuming:
- A is at (0, 1)
- B is at (1, 1)
- C is at (1, 0)
- D is at (0, 0)
After a 90° clockwise rotation:
- A' (0, 1) becomes (1, 0)
- B' (1, 1) becomes (1, -1)
- C' (1, 0) becomes (0, -1)
- D' (0, 0) remains (0, 0)
The points after rotation will still form a square.
Now, in terms of angles, each angle of the original square ABCD measures 90°. After rotation, the angles at each vertex of the new square A'B'C'D' will still measure 90°.
Thus, angle B' is: B. 90°