Question 1: Calculate the coordinates of a point (3, 4) after a 90° rotation about the origin with a negative scale factor of -1.

Answer: (-4, 3)

Question 2: Rotate the point (5, -2) 180° about the origin. What are the new coordinates?

Answer: (-5, 2)

Question 3: A point (-6, 1) is rotated 270° counter-clockwise about the origin. Find its new position.

Answer: (1, 6)

Question 4: Construct the rotation of point (2, -3) by 360° about the origin on the grid. What are the coordinates after rotation?

Answer: (2, -3)

Question 1: A triangle with vertices at (1, 2), (4, 2), and (1, 5) is rotated 180° about the origin. Describe the new positions of the vertices and explain why the shape appears unchanged but inverted.

Answer: Vertices become (-1, -2), (-4, -2), (-1, -5); shape rotated upside down, maintaining size but reversed orientation.

Question 2: Explain the error in the following statement: 'Rotating a point (-3, 4) by 90° clockwise with a negative scale factor will give the same result as rotating it 90° counter-clockwise.'

Answer: Incorrect because a negative scale factor combined with rotation changes the typical direction; rotation direction depends on angle, not sign of scale factor.

Question 3: A point is rotated 270° clockwise about the origin with a negative scale factor of -1. What is the final position? Show your working.

Answer: (4, 3)

Question 1: A satellite dish is rotated 90° clockwise from its original position at (0, 5). What are the new coordinates of the dish? Why might errors occur if the rotation is done incorrectly?

Answer: (5, 0); errors may include incorrect angle direction or not accounting for negative scale factors.

Question 1: Construct a square with vertices at (1,1), (4,1), (4,4), (1,4). Rotate it 360° with a negative scale factor of -1 and describe the resulting figure. Explain why the shape appears unchanged but inverted.

Answer: Square remains the same size and shape, but inverted over the origin. Coordinates are reflected across the origin.

Question 1: Rotate the point (-2, 5) 90° clockwise about the origin. Show the calculation process.

Answer: (-5, -2)

Question 2: If a point (x, y) is rotated 180° about the origin with a negative scale factor, what is the general formula for the new coordinates?

Answer: (-x, -y)

Question 1: A student claims that rotating a point (3, -4) by 90° with a negative scale factor of -1 will result in (4, 3). Identify the mistake and provide the correct coordinates.

Answer: Incorrect because rotation by 90° swaps coordinates; correct position is (4, 3) but the mistake was in assuming the negative scale factor affects rotation direction. Correct answer: (-4, -3).

Question 2: A student rotates the point (-5, 2) by 180° incorrectly, assuming the coordinates become (5, -2). What is the actual result and why?

Answer: Actual result is (5, -2); the mistake is in the direction of rotation; 180° rotation about the origin simply negates both coordinates.