Square ABCD is shown.

If square ABCD were rotated 90° clockwise about the origin to create square A'B'C'D', what would the measure of angle B' be?
A.
45°
B.
90°
C.
180°
D.
270°

1 answer

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°