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

Answer: (-4, 3)

Question 2: Rotate the point (-5, 2) 90° anticlockwise about the origin. What are the coordinates of the image?

Answer: (-2, -5)

Question 3: A triangle has vertices at A(2, 1), B(4, 3), and C(3, 5). Plot and then rotate the triangle 90° anticlockwise about the origin. State the new coordinates of each vertex.

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

Question 4: If a point P is at (x, y), write the formula for the coordinates of P' after a 90° anticlockwise rotation about the origin.

Answer: P'(–y, x)

Question 1: A rectangle has vertices at (1, 2), (5, 2), (5, 4), and (1, 4). Rotate the rectangle 90° anticlockwise about the origin. What are the new coordinates of the vertices?

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

Question 2: A shape with points at (2, 3), (4, 3), and (4, 5) is rotated 90° anticlockwise about the origin. Describe the transformation process and find the image points.

Answer: Each point swaps coordinates with a change of sign: (2, 3) → (–3, 2); (4, 3) → (–3, 4); (4, 5) → (–5, 4).

Question 3: A point P is at (–3, 4). If P’ is the image after rotation about the origin, what are the coordinates of P’? Also, verify the rotation by plotting the points.

Answer: (–4, –3)

Question 4: Explain why the point (x, y) transforms to (–y, x) after a 90° anticlockwise rotation about the origin.

Answer: Because the rotation swaps x and y, with y becoming negative to account for the anticlockwise direction.

Question 1: A drone is flying at point (6, 2). It makes a 90° anticlockwise turn around the origin. Where does the drone end up?

Answer: (–2, 6)

Question 2: A city park has a sculpture at (3, 3). The sculpture is rotated 90° anticlockwise about the origin for a new display. Find the new position of the sculpture.

Answer: (–3, 3)

Question 1: A pentagon has vertices at (1, 1), (2, 3), (4, 3), (5, 1), and (3, –1). Rotate the pentagon 90° anticlockwise about the origin. Determine the coordinates of the new vertices.

Answer: A'(–1, 1), B'(–3, 2), C'(–3, 4), D'(–1, 5), E'(1, 3)

Question 2: Given a shape with points at (–2, 7), (0, 5), and (2, 7), explain how rotating 90° anticlockwise about the origin affects its shape and position. Find the new coordinates.

Answer: Points become (–7, –2), (–5, 0), and (–7, 2). The shape rotates counterclockwise, maintaining its form, but position changes.

Question 1: Identify the error: A student claims that rotating (x, y) 90° anticlockwise about the origin results in (y, –x). Is this correct? Correct the mistake if any.

Answer: Incorrect. The correct transformation is (–y, x).

Question 2: Plot the points (1, 2), (3, 4), and (5, 6). Rotate them 90° anticlockwise on the grid. Confirm the new positions.

Answer: (–2, 1), (–4, 3), (–6, 5)