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

Answer: (4, -3)

Question 2: Construct the image of the point (-2, 5) after rotating it 90° clockwise about the origin. Write the new coordinates.

Answer: (5, 2)

Question 3: A point P has coordinates (0, -6). What are its coordinates after a 90° rotation clockwise about the origin?

Answer: (-6, 0)

Question 4: Plot the point (2, -3) on the grid. Then, rotate it 90° clockwise about the origin and mark its new position.

Answer: ( -3, -2 )

Question 5: A triangle has vertices at A(1, 2), B(3, 4), and C(5, 0). Construct the image of this triangle after a 90° clockwise rotation about the origin. List the new coordinates.

Answer: A'(2, -1), B'(4, -3), C'(0, -5)

Question 6: Explain why the point (-7, 0) maps to (0, 7) after a 90° clockwise rotation about the origin.

Answer: Because rotating 90° clockwise swaps the x and y coordinates and changes the sign of the new x-coordinate, so (-7, 0) becomes (0, 7).

Question 7: Determine the image of the point (0, -9) after rotation about the origin by 90° clockwise.

Answer: ( -9, 0 )

Question 8: Construct a point at (-4, 1). Rotate it 90° clockwise about the origin and record its coordinates.

Answer: (1, 4)

Question 9: A square has vertices at (1, 1), (1, 3), (3, 3), and (3, 1). Find the new coordinates after rotating the square 90° clockwise about the origin.

Answer: (1, -1), (3, -1), (3, 1), (1, 1)

Question 10: Identify and correct the mistake in the following student solution: The student claims that rotating (5, -2) 90° clockwise about the origin results in (-2, 5).

Answer: The correct coordinates after rotation are (-2, -5). The student forgot to change the sign of the y-coordinate.

Question 11: Challenge: Find the original point if after a 90° clockwise rotation about the origin, the point (3, -4) is obtained.

Answer: (-4, -3)