Question 1: Calculate the coordinates of the point (3, 5) after a 90° clockwise rotation about the origin.

Answer: (5, -3)

Question 2: A point P is at (-4, 2). Find the coordinates of P after rotation about the origin by 90° clockwise.

Answer: (2, 4)

Question 3: Plot the point (-1, 3) and then rotate it 90° clockwise about the origin. Write down the new coordinates.

Answer: (3, 1)

Question 4: What is the image of the point (0, -6) after a 90° clockwise rotation about the origin?

Answer: (-6, 0)

Question 1: A triangle has vertices at A(2, 4), B(6, 2), and C(4, 0). After rotating all vertices 90° clockwise about the origin, what are the new coordinates of the triangle’s vertices?

Answer: A'(4, -2), B'(2, -6), C'(0, -4)

Question 2: Explain why the point (x, y) moves to the point (y, -x) after a 90° clockwise rotation about the origin.

Answer: Because a 90° clockwise rotation swaps the coordinates and negates the original x-coordinate, transforming (x, y) to (y, -x).

Question 3: A point (1, -2) is rotated 90° clockwise about the origin. Find its image and describe the transformation.

Answer: The image is (-2, -1). The transformation swaps x and y and negates the new x-coordinate.

Question 4: If a figure has vertices at (2, 3), (4, 5), and (6, 3), determine the coordinates after a 90° clockwise rotation about the origin and verify the shape is congruent.

Answer: Vertices become (3, -2), (5, -4), (3, -6). The shape remains congruent with rotated vertices.

Question 1: A robot at point (4, 1) in a grid moves to a new position after rotating 90° clockwise about the origin. What are the new coordinates? How could this movement be useful in grid navigation?

Answer: The new position is (1, -4). This rotation is useful in navigation algorithms to change orientation without changing position.

Question 1: A point moves from (x, y) to (y, -x) after rotation. Find the original coordinates if the image point is at (-3, 4).

Answer: (4, 3)

Question 2: Construct a triangle on the grid with vertices at (1, 2), (3, 4), and (5, 2). Rotate the triangle 90° clockwise about the origin and describe the change in area.

Answer: Vertices become (2, -1), (4, -3), (2, -5). The area remains unchanged as rotation preserves size.

Question 1: A point (0, 7) is rotated 90° clockwise. What are its new coordinates?

Answer: (7, 0)

Question 2: Describe the geometric effect of a 90° clockwise rotation about the origin on a point and its position relative to the axes.

Answer: It swaps the x and y coordinates and negates the new x, effectively rotating the point clockwise and maintaining the same distance from the origin.

Question 1: A student claims that rotating (3, -2) 90° clockwise about the origin results in (2, 3). Is this correct? If not, what is the correct image?

Answer: Incorrect. The correct image is (-2, -3).

Question 2: A common mistake is to swap coordinates without negating. Explain why this is incorrect for a 90° clockwise rotation about the origin.

Answer: Swapping coordinates alone reflects a 90° counter-clockwise rotation. For clockwise rotation, the x-coordinate must be negated after swapping.