Question 1: Reflect the point (3, -4) across the line y = -x. Write down the new coordinates.

Answer: (-4, 3)

Question 2: What is the result of swapping and negating the point (7, -2)?

Answer: (-2, -7)

Question 3: Perform the reflection of the point (-5, 6) across y = -x. Provide the reflected point.

Answer: ( -6, 5)

Question 4: Calculate the new coordinates after swapping and negating (0, -9).

Answer: (9, 0)

Question 5: Plot the graph of y = 2x. Using the grid, mark the points (1, 2), (-2, -4), and (3, 6).

Answer: Coordinates plotted correctly

Question 6: Construct a triangle with vertices at (2, 3), (4, -1), and (0, 0). Reflect each vertex across y = -x and label the new vertices.

Answer: Vertices at (-3, 2), (-1, 4), and (0, 0)

Question 7: A point is at (x, y). If after swapping and negating, it becomes (-x, -y), what is the original point?

Answer: The original point is (-x, -y)

Question 8: A reflection of the point (8, -3) across y = -x results in which point? Show your working.

Answer: (-3, 8)

Question 9: Identify and correct the mistake: The point (5, -7) reflected across y = -x was written as (-5, 7).

Answer: Incorrect, the correct reflection is (-7, 5)

Question 10: If a point moves from (x, y) to (-y, -x) after reflection, what can you say about its original position relative to the line y=-x?

Answer: The original point is the image of the reflection of (-y, -x) across y = -x

Question 11: Challenge: Find a point (x, y) that, after swapping and negating, results in the point (y, x). What does this imply about the original point?

Answer: It implies the point is on the line y = -x