Question 1: What are the coordinates of the point (3, -4) after rotating 180° about the origin?

Answer: (-3, 4)

Question 2: Plot the point (-2, 5) and its image after a 180° rotation about the origin on the grid.

Answer: (-2, 5) → (2, -5)

Question 3: If a point P has coordinates (x, y), write the formula to find its image P' after a 180° rotation about the origin.

Answer: P' = (-x, -y)

Question 4: A point is at (7, -3). What are its coordinates after rotating 180° about the origin?

Answer: (-7, 3)

Question 5: Construct a triangle with vertices at (1, 2), (4, 2), and (1, 5). Then, reflect the triangle by rotating 180° about the origin. Describe the new coordinates of each vertex.

Answer: Vertices after rotation: (-1, -2), (-4, -2), (-1, -5)

Question 6: Identify the common mistake made when rotating a point (x, y) by 180° about the origin. How can it be avoided?

Answer: Mistake: Reversing only one coordinate or misapplying the rule. It can be avoided by remembering the rule P' = (-x, -y).

Question 7: A point has coordinates (0, -6). Find its image after a 180° rotation about the origin.

Answer: (0, 6)

Question 8: A student mistakenly rotates the point (4, -5) to (4, 5) instead of the correct image. Identify the error and explain the correct rotation.

Answer: Error: They only changed the y-coordinate, not both coordinates. The correct image after 180° rotation is (-4, 5).

Question 9: Plot and rotate the point (-3, 2) by 180° about the origin. What are the new coordinates?

Answer: (-3, 2) → (3, -2)

Question 10: Find the image of the point (–1, 0) after rotating 180° about the origin. Then, verify by calculation.

Answer: (1, 0)

Question 11: A rectangle has vertices at (2, 3), (5, 3), (5, 6), and (2, 6). What are the vertices after rotating 180° about the origin?

Answer: Vertices: (-2, -3), (-5, -3), (-5, -6), (-2, -6)