Question 1: Plot the point (3, 2) on the grid. Rotate it 90° anticlockwise about the origin and write down the new coordinates.

Answer: (2, -3)

Question 2: A triangle has vertices at (1, 4), (4, 2), and (2, 1). Construct the triangle and then rotate it 90° anticlockwise about the origin. Record the new coordinates of the vertices.

Answer: Vertices after rotation: (-4, 1), (-2, 4), (-1, 2)

Question 3: What is the rule for rotating a point (x, y) 90° anticlockwise about the origin?

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

Question 4: Plot the point (-5, 3). Rotate it 90° anticlockwise about the origin and write down its new coordinates.

Answer: (3, 5)

Question 5: A rectangle has vertices at (2, 1), (5, 1), (5, 4), and (2, 4). Construct the rectangle and perform a 90° anticlockwise rotation about the origin. List the new coordinates.

Answer: Vertices after rotation: (-1, 2), (-1, 5), (-4, 5), (-4, 2)

Question 6: Explain why the point (0, 5) stays on the same line after a 90° anticlockwise rotation about the origin.

Answer: Because it is on the y-axis, and rotation about the origin moves points on axes accordingly, but (0, y) becomes (-y, 0), which for (0, 5) results in (-5, 0).

Question 7: Construct a right-angled triangle with vertices at (1, 1), (4, 1), and (1, 4). Rotate it 90° anticlockwise about the origin. What are the new coordinates?

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

Question 8: A real-world scenario: A car parked at point (3, 2) needs to be moved by rotating it 90° anticlockwise about the origin. If the car's front is at (3, 2), where will it be after rotation?

Answer: The front will be at (2, -3).

Question 9: Identify and correct the mistake in this rotation: A student rotates the point (4, -3) and claims the new point is (-3, -4). Is this correct? Explain.

Answer: No, the correct rotation of (4, -3) 90° anticlockwise is (3, 4). The student's answer swaps coordinates incorrectly.

Question 10: Construct a parallelogram with vertices at (1, 1), (4, 1), (3, 4), and (0, 4). Rotate it 90° anticlockwise about the origin and record the new vertices.

Answer: Vertices after rotation: (-1, 1), (-1, 4), (-4, 3), (-4, 0)

Question 11: Challenge: If a line passes through the points (2, 3) and (4, 5), find the new coordinates of these points after rotating 90° anticlockwise about the origin. Then, find the equation of the new line.

Answer: New points: (-3, 2) and (-5, 4). Equation of line: y = x + 1.