Question 1: Calculate the coordinates of the point (3, 4) after a 90° anticlockwise rotation about the origin.

Answer: (-4, 3)

Question 2: Rotate the point (-2, 5) 90° anticlockwise about the origin. Write down the new coordinates.

Answer: (-5, -2)

Question 3: Plot the point (1, -3) on the grid. Then, rotate it 90° anticlockwise about the origin and mark the new position.

Answer: New position at (3, 1)

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

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

Question 5: Explain why rotating a point (x, y) 90° anticlockwise about the origin results in (-y, x).

Answer: Because the rotation swaps and negates the coordinates according to the rotation matrix for 90° anticlockwise.

Question 6: A point moves from (5, -2) to its new position after rotation. Find the new coordinates.

Answer: (2, 5)

Question 7: A real-world object located at (x, y) on a coordinate grid is rotated 90° anticlockwise about the origin. If the original position is at (x, y), what is its new position?

Answer: (-y, x)

Question 8: Identify and correct the mistake in this rotation: The point (3, 4) was rotated 90° clockwise about the origin, ending at (4, -3).

Answer: The rotation was clockwise, but the problem asks for anticlockwise; also, the correct position after 90° anticlockwise should be (4, -3) for clockwise rotation.

Question 9: A square has vertices at (1,1), (1,3), (3,3), and (3,1). Rotate the square 90° anticlockwise about the origin. What are the new vertices?

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

Question 10: For the point (-5, 0), perform a 90° anticlockwise rotation about the origin and determine its new position.

Answer: (0, -5)