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

Answer: (-4, 3)

Question 2: Plot the point Q(−2, 5) on the grid and then rotate it 90° anticlockwise about the origin. Write the coordinates of Q' after rotation.

Answer: (-5, -2)

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

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

Question 4: Explain why the points on the x-axis or y-axis do not change their position when rotated 90° about the origin.

Answer: Because points on the axes lie on the rotation axis and remain fixed during rotation.

Question 1: Point R(6, −2) is rotated 90° anticlockwise about the origin. Then, it is reflected across the y-axis. Find the final coordinates of R after both transformations.

Answer: (2, 6)

Question 2: A square with vertices at (2, 1), (2, 4), (5, 4), and (5, 1) is rotated 90° anticlockwise about the origin. What are the new coordinates of the vertices?

Answer: (-1, 2), (4, 2), (4, 5), (-1, 5)

Question 3: A vehicle at position (x, y) starts at point (3, −4). It then moves to a new position after a 90° anticlockwise rotation about the origin and a translation of 2 units right and 3 units up. Find the final position of the vehicle.

Answer: (1, 1)

Question 1: A drone flying at point (−3, 2) needs to change its direction to head east after executing a 90° anticlockwise rotation about the origin. Where will the drone be after the rotation?

Answer: The drone will be at (−2, 3).

Question 2: A delivery truck at (4, −3) plans to rotate its route map 90° anticlockwise about the depot at the origin. What are the new coordinates for the truck’s position?

Answer: (3, 4)

Question 1: A rectangle with vertices at (1, 1), (1, 4), (5, 4), and (5, 1) is rotated 90° anticlockwise about the origin, then reflected across the x-axis. Find the final coordinates of all vertices.

Answer: (-1, -1), (-1, -4), (-5, -4), (-5, -1)

Question 2: Design a path for a robot starting at (2, 2), which moves to a point after a 90° anticlockwise rotation, then back to the original position using the inverse rotation. Describe the sequence of coordinates.

Answer: Start at (2, 2), rotate to (−2, 2), then rotate back to (2, 2).

Question 1: Point S(−1, −3) is rotated 90° anticlockwise about the origin. What are the new coordinates?

Answer: (3, −1)

Question 2: Identify the mistake: A student claimed that rotating any point (x, y) 90° anticlockwise about the origin results in (y, x). Explain and correct the mistake.

Answer: The correct rotation results in (−y, x), not (y, x).