Question 1: A square window on a building is located with its bottom-left corner at (2, 3). If the window is rotated 90° clockwise about the origin, what will be the coordinates of its bottom-left corner?

Answer: (3, -2)

Question 2: Construct a rectangle with vertices at (1, 1), (4, 1), (4, 3), and (1, 3). Rotate this rectangle 90° clockwise about the origin. Draw and label the new position of the rectangle on the grid.

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

Question 3: A triangular arch in a park has vertices at (2, 4), (5, 4), and (3.5, 6). If the arch is rotated 90° clockwise about the origin, what are the new coordinates of the vertices?

Answer: (4, -2), (4, -5), (6, -3.5)

Question 4: A building facade includes a rectangular sign with bottom-left corner at (3, -2). The sign is rotated 90° clockwise about the origin. What are the coordinates of the bottom-left corner after rotation?

Answer: (-2, -3)

Question 5: A design plan involves rotating a pattern with points at (1, 2), (2, 4). Calculate the new positions after a 90° clockwise rotation about the origin.

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

Question 6: Explain why rotating a shape 90° clockwise about the origin changes the coordinates from (x, y) to (y, -x).

Answer: Because a 90° clockwise rotation swaps the x and y coordinates and negates the new x-coordinate, resulting in (y, -x).

Question 7: A rectangular window positioned at (−4, 1) is rotated 90° clockwise about the origin. What's the new position of this window?

Answer: (1, 4)

Question 8: Construct a triangle with vertices at (0, 0), (3, 0), and (1.5, 3). Use the grid to draw the triangle. Then rotate it 90° clockwise about the origin and draw the new triangle.

Answer: Vertices after rotation: (0, 0), (0, -3), (1.5, -3)

Question 9: A design feature has a pattern with points at (5, 2), (6, 4). After rotating 90° clockwise about the origin, where are these points located?

Answer: (2, -5), (4, -6)

Question 10: A mistake in a rotation is that someone used (x, y) to (−x, y). Identify and explain the error made in rotating a shape 90° clockwise about the origin.

Answer: The error is using (−x, y) instead of (y, -x); the correct rotation swaps x and y and negates the new x.