Question 1: Rotate the point (3, 4) about the origin by 180°. What are the coordinates of the image?

Answer: (-3, -4)

Question 2: Construct the rotation of the point (2, -1) about the origin by 180° on the grid.

Answer: (-2, 1)

Question 3: If a point P is located at (5, 2) and is rotated 180° about the point (1, 0), what are the coordinates of P'?

Answer: (−3, -2)

Question 4: Explain the rule for rotating a point (x, y) by 180° about the origin.

Answer: The coordinates become (-x, -y).

Question 5: A triangle has vertices at A(1, 2), B(4, 5), and C(2, 4). Construct the image of the triangle after a 180° rotation about the origin.

Answer: A'(-1, -2), B'(-4, -5), C'(-2, -4)

Question 6: A point P(−3, 6) is rotated 180° about the point (1, 2). Find the coordinates of P'.

Answer: (5, -2)

Question 7: Describe a real-world scenario where understanding rotation about a point by 180° might be useful.

Answer: Rotating a picture or object in graphic design or engineering layouts.

Question 8: Given the point Q(−2, 3), rotate it 180° about the point (0, 0). Confirm the coordinates.

Answer: (2, -3)

Question 9: Construct a square with vertices at (1, 1), (1, 3), (3, 3), and (3, 1). Rotate it 180° about the center (2, 2). What are the new vertices?

Answer: Vertices after rotation: (3, 1), (3, 3), (1, 3), (1, 1)

Question 10: Identify and correct the mistake in this rotation: Rotating point (4, −5) 180° about the origin was incorrectly performed as (−4, 5).

Answer: The correct coordinates are (−4, 5); the mistake was assuming the rotation changes signs incorrectly—rotation by 180° about the origin results in (−x, −y).

Question 11: A shape is rotated 180° about the origin. The original point was at (−7, 2). What is the location of the image?

Answer: (7, -2)