Question 1: What are the coordinates of point A(3, 4) after a 90° clockwise rotation about the origin?

Answer: (4, -3)

Question 2: Calculate the new coordinates of point B(-2, 5) after a 90° clockwise rotation about the origin.

Answer: (5, 2)

Question 3: Plot the point C(0, -6) on the grid and then draw its 90° clockwise rotation about the origin.

Answer: (6, 0)

Question 4: A triangle has vertices at P(2, 3), Q(4, 1), and R(3, 4). Construct the image of this triangle after a 90° clockwise rotation about the origin.

Answer: P(3, -2), Q(1, -4), R(4, -3)

Question 5: A point D lies at (5, -2). What are its coordinates after a 90° clockwise rotation about the origin?

Answer: (-2, -5)

Question 6: Identify the mistake in this rotation process: A point at (1, 2) is rotated 90° clockwise and the new point is given as (2, 1). Is this correct? Why or why not?

Answer: No, the correct new point should be (2, -1). The mistake is in the sign of the y-coordinate.

Question 7: Construct the point (x, y) such that after a 90° clockwise rotation about the origin, it lands at (7, -3). What are the original coordinates?

Answer: (3, 7)

Question 8: Explain why rotating a point (x, y) 90° clockwise about the origin results in the point (y, -x).

Answer: Because the rotation swaps x and y coordinates and applies a negative sign to the new x-coordinate, following the rotation rule.

Question 9: A square has vertices at (1, 1), (1, 3), (3, 3), and (3, 1). Plot and rotate this square 90° clockwise about the origin. What are the new coordinates?

Answer: Vertices after rotation: (1, -1), (3, -1), (3, -3), (1, -3)

Question 10: Challenge: Given a point (x, y) such that after a 90° clockwise rotation it falls at (0, -2), find all possible original points.

Answer: Possible original points: (2, 0) and (-2, 0)

Question 11: Identify and correct the error in this rotation: Point (4, -3) is rotated 90° clockwise to (3, 4).

Answer: Incorrect. The correct rotated point should be (-3, -4). The error is in the sign of the x-coordinate.