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

Answer: (-3, -4)

Question 2: Calculate the coordinates of point Q at (5, -2) after rotating 180° about point R at (2, 3).

Answer: (0, 5)

Question 3: A triangle has vertices at A(1, 2), B(4, 3), and C(2, 5). If the triangle is rotated 180° about point (2, 3), what are the new coordinates of A, B, and C?

Answer: A(-1, 4), B(0, 3), C(2, 1)

Question 4: A real-world scenario: A drone is flying at point (10, 4). It needs to fly to a new position after rotating 180° about a stationary tower at (6, 2). Find the drone's new coordinates.

Answer: (2, 0)

Question 5: Plot the graph of y=2x and then plot the point (3, 6). Rotate the point 180° about the origin and mark the new position on the grid.

Answer: (-3, -6)

Question 6: Construct a triangle on the grid with vertices at (2, 2), (4, 2), and (3, 4). Rotate this triangle 180° about point (3, 3). Record the new vertices.

Answer: A(4, 4), B(2, 4), C(3, 2)

Question 7: A mirror image of a point P(7, 1) is created by rotating 180° about point (5, 3). What are the coordinates of the reflected point?

Answer: (3, 5)

Question 8: Identify and correct the mistake in this student’s rotation: A student claims that rotating point (2, 3) 180° about (1, 1) results in (0, 2).

Answer: Correct coordinates are (0, -1); the student added instead of subtracting the change.

Question 9: A painting is hung on a wall at point (4, 5). It is rotated 180° about a pivot point at (2, 2). What are the new coordinates of the painting?

Answer: (0, -1)

Question 10: Challenge: A robot starts at (8, 7) and rotates 180° about point (3, 4). Afterwards, it moves to (5, 0). What was its original position before the rotation?

Answer: (-2, 1)