Question 1: If a point P is at (3, 4), what are its coordinates after a 180° rotation about the origin?

Answer: (-3, -4)

Question 2: Plot the point (–2, 5) on the grid. Then, plot its image after a 180° rotation about the origin. Label both points clearly.

Answer: Plot (–2, 5) and (2, –5).

Question 3: Calculate the coordinates of the point (–6, –1) after rotating 180° about the origin.

Answer: (6, 1)

Question 4: A triangle with vertices at A(2, 3), B(4, –1), and C(–1, –2) is rotated 180° about the origin. Find the new coordinates of each vertex.

Answer: A'(–2, –3), B'(–4, 1), C'(1, 2)

Question 5: If a figure is rotated 180° about the origin and appears upside down, what can you say about its original orientation?

Answer: It was upside down or inverted relative to its position after rotation.

Question 6: Construct a rectangle on the grid with vertices at (1, 1), (4, 1), (4, 3), and (1, 3). Rotate it 180° about the origin and label the new vertices.

Answer: Vertices at (–1, –1), (–4, –1), (–4, –3), (–1, –3).

Question 7: A point moves from (–3, 7) to its new position after a 180° rotation. What is its new position?

Answer: (3, –7)

Question 8: Explain why rotating a point 180° about the origin results in the point being directly opposite to its original position.

Answer: Because rotating 180° about the origin moves the point to the exact opposite side, reflecting both coordinates.

Question 9: Identify and correct the mistake in this statement: 'Rotating a point (x, y) 180° about the origin results in the point (x, y).'

Answer: The correct image is (–x, –y); the original point remains unchanged only if it is at the origin.

Question 10: A point (4, –3) is rotated 180°. What are the new coordinates?

Answer: (–4, 3)

Question 11: A figure is rotated 180° about the origin. Describe a real-world scenario where this type of rotation might be used.

Answer: Turning a map upside down to view the opposite direction or orientation.