Question 1: Rotate the point (3, 4) 90° anticlockwise about the origin. Write down the new coordinates.

Answer: (-4, 3)

Question 2: A triangle has vertices at A(2, 1), B(4, 3), and C(3, 5). Rotate the triangle 90° anticlockwise about the origin. List the new coordinates of A', B', and C'.

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

Question 3: Plot the point (-2, 5) on the grid. Then rotate it 90° anticlockwise about the origin and mark the new position.

Answer: (5, 2)

Question 4: Construct a rectangle with vertices at (1, 1), (4, 1), (4, 3), and (1, 3). Rotate the rectangle 90° anticlockwise about the origin. Draw and label the new rectangle.

Answer: Vertices after rotation: (-1, 1), (-1, 4), (-3, 4), (-3, 1)

Question 5: A point is located at (0, -6). What are its coordinates after a 90° anticlockwise rotation about the origin?

Answer: (6, 0)

Question 6: Describe the rule for rotating any point (x, y) 90° anticlockwise about the origin.

Answer: The point (x, y) becomes (-y, x).

Question 7: A square has vertices at (2, 2), (2, 4), (4, 4), and (4, 2). Rotate the square 90° anticlockwise about the origin. What are the new coordinates of the vertices?

Answer: (-2, 2), (-4, 2), (-4, 4), (-2, 4)

Question 8: Identify and correct the mistake in this rotation: The point (3, -2) is rotated 90° anticlockwise about the origin, and the answer given is (2, 3).

Answer: Incorrect; the correct coordinates are (2, 3). The mistake is in the rule: (x, y) should become (-y, x); here, (-(-2),3) = (2, -3).

Question 9: A kite has vertices at (0, 0), (2, 2), (4, 0), and (2, -2). Rotate the kite 90° anticlockwise about the origin. Provide the new coordinates.

Answer: A'(0, 0), B'(-2, 2), C'(0, 4), D'(2, 0)

Question 10: Challenge: A triangle has vertices at (1, 2), (3, 4), and (5, 0). Rotate it 90° anticlockwise about the origin twice. What are the final coordinates?

Answer: First rotation: (-2, 1), (-4, 3), (0, 5); Second rotation: (-1, -2), (-3, -4), (-5, 0)