Question 1: A point P(3, 4) is rotated 90° anticlockwise about the origin. What are the coordinates of the image point P'?

Answer: P'(-4, 3)

Question 2: Construct the rotation of the point (-2, 5) about the origin by 90° anticlockwise. Write the new coordinates.

Answer: (-5, -2)

Question 3: If a point (x, y) is rotated 90° anticlockwise about the origin, what is the formula to find the new coordinates?

Answer: (-y, x)

Question 4: A student incorrectly claims that rotating (1, -3) by 90° anticlockwise gives (3, 1). Identify and explain the mistake.

Answer: Incorrectly applying the rotation formula; the correct image is (3, 1), but the student swapped coordinates without changing signs properly.

Question 5: Plot the point (4, -2) on the grid, rotate it 90° anticlockwise about the origin, then label the new position.

Answer: Coordinates after rotation: (2, 4)

Question 6: A shape is rotated 90° anticlockwise about the origin. The point A(1, 2), B(3, 4), and C(-2, 1) are vertices. Find the new positions of these points.

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

Question 7: A diagram shows a point at (x, y). The student claims that after a 90° anticlockwise rotation, the new point is at (x, y). Explain why this is incorrect.

Answer: Because the rotation changes the position unless the point is at the origin; the correct coordinates are (-y, x).

Question 8: Identify the common misconception: Some students think that rotating a point (x, y) by 90° clockwise about the origin results in (-y, x). Is this correct? Why or why not?

Answer: No, because (-y, x) is the result of a 90° anticlockwise rotation; clockwise rotation would give (y, -x).

Question 9: A point (5, -1) is rotated 90° anticlockwise. What is the resulting coordinate? Show your working.

Answer: (-(-1), 5) = (1, 5)

Question 10: A student attempts to rotate the point (0, 0) by 90° about the origin. What is the image? Explain your reasoning.

Answer: The image is (0, 0) because rotating the origin about itself leaves it unchanged.

Question 11: Challenge: Find all points on the circle x² + y² = 25 that map onto themselves after a 90° anticlockwise rotation about the origin. Explain your reasoning.

Answer: Points on the axes at (±5, 0) and (0, ±5) are fixed; others move to different locations.