Question 1: Rotate the point (3, 4) 90° clockwise about the origin. What are the coordinates of the image?

Answer: (4, -3)

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

Answer: (2, 5)

Question 3: Rotate the point (0, -6) 90° clockwise about the origin. Find the new position.

Answer: (-6, 0)

Question 4: What is the rule for rotating a point (x, y) 90° clockwise about the origin?

Answer: Transform (x, y) to (y, -x).

Question 1: A point P(7, -3) is rotated 90° clockwise about the origin. The image is point Q. If Q is at (3, 7), is this correct? Explain your reasoning and correct the mistake if any.

Answer: No, the correct image should be (-3, -7). The mistake is applying the rotation rule incorrectly.

Question 2: A student claims rotating (x, y) 90° clockwise about the origin results in (x, y). Is this correct? Why or why not?

Answer: No, because the rule transforms (x, y) to (y, -x), which generally changes the point.

Question 3: Given a point (x, y), describe the steps to accurately rotate it 90° clockwise about the origin.

Answer: Swap the coordinates to (y, x) and then change the sign of the new x-coordinate to negative, resulting in (y, -x).

Question 1: A drone starts at point (2, 3) and is rotated 90° clockwise about the origin to reach a new position. Its new position is directly south of its original position. Find the new coordinates.

Answer: (-3, 2)

Question 2: A robot moves from (4, -5). After rotating 90° clockwise about the origin, it ends up at (5, 4). Is this consistent with the rotation rule? Explain.

Answer: Yes, rotating (4, -5) gives (-5, -4). The resulting point (5, 4) is incorrect; the correct image is (-5, -4).

Question 1: Construct the image of the point (-6, 8) after a 90° clockwise rotation about the origin. Confirm whether your construction matches the rule.

Answer: (-8, -6)

Question 2: Prove that rotating any point (x, y) 90° clockwise is equivalent to multiplying the vector by a rotation matrix. Provide the matrix and demonstrate the transformation.

Answer: The rotation matrix is [[0, 1], [-1, 0]]. Multiplying (x, y) by this matrix yields (y, -x).

Question 1: A student states that rotating (x, y) 90° clockwise results in (x, y). Is this correct? If not, what is the mistake?

Answer: Incorrect, because the correct transformation is (y, -x). The mistake is assuming the point stays the same.

Question 2: A teacher claims that rotating (0, y) 90° clockwise results in (0, -y). Is this true? Explain.

Answer: No, rotating (0, y) gives (y, 0), not (0, -y). The mistake is misapplying the rule.