Question 1: Plot the point (3, 4) on the grid. Then, rotate it 180° about the origin. What are the coordinates of the new point?

Answer: -3, -4

Question 2: A point at (-6, 2) is rotated 180° about the origin. What are its new coordinates?

Answer: 6, -2

Question 3: Construct a point at (0, -5). Rotate it 180° about the origin and describe the change in position.

Answer: The point moves from (0, -5) to (0, 5), flipping across the origin along the y-axis.

Question 4: Plot the point (–4, –3). Confirm its 180° rotation about the origin. What is the resulting point?

Answer: 4, 3

Question 1: Explain why rotating a point (x, y) about the origin by 180° results in the point (–x, –y).

Answer: Because a 180° rotation about the origin flips both the x and y coordinates, changing their signs.

Question 2: Given a point (x, y) = (7, –8), find its rotation after 180° about the origin without plotting. Show your calculation.

Answer: –7, 8

Question 3: If a student mistakenly believes that rotating (x, y) by 180° results in (x, y), identify the error and correct it.

Answer: The student is incorrect; the correct rotation results in (–x, –y), not the same point.

Question 4: Prove algebraically that a point (x, y) rotated 180° about the origin gives (–x, –y).

Answer: Using rotation rules: (x, y) → (–x, –y).

Question 1: A drone is at position (10, –4). It moves through a 180° rotation about its starting point. What are its new coordinates?

Answer: –10, 4

Question 2: A robot at (–2, 7) performs a 180° rotation about the origin. If the robot moves to the new position, describe its movement as a reflection.

Answer: It reflects across both axes, moving to (2, –7).

Question 1: Construct a triangle with vertices at (1, 2), (3, 4), and (5, 0). Rotate the entire triangle 180° about the origin. List the new vertices.

Answer: -1, -2; -3, -4; -5, 0

Question 2: A mirror image across the origin is a 180° rotation. Find the image of the point (–9, 3). Explain the geometric reasoning.

Answer: The image is (9, –3). Reflection across both axes results in negating both coordinates.

Question 1: A student claims that rotating (x, y) by 180° results in (x, y). Identify and correct the misconception.

Answer: They are mistaken; the correct rotation is (–x, –y).

Question 2: Common mistake: A student rotates (4, –3) and gets (4, –3) again. What is the error?

Answer: They did not change the signs; the correct result should be (–4, 3).

Question 3: Explain how misapplying the rule for 180° rotation leads to incorrect answers, with an example.

Answer: Misapplying the rule, such as leaving coordinates unchanged, results in incorrect answers; the correct rule is (x, y) → (–x, –y).