Question 1: Reflect the point (3, -5) over the line y = -x. What are the new coordinates?

Answer: 5, -3

Question 2: What is the reflection of the point (-2, 4) over y = -x?

Answer: 4, 2

Question 3: Plot the point (1, -3) and reflect it over y = -x on the grid.

Answer: Point (1, -3) reflected over y = -x is at (-3, -1).

Question 4: A triangle has vertices at (2, 3), (4, -1), and (0, 0). Reflect all vertices over y = -x and list the new coordinates.

Answer: (-3, 2), (-1, 4), (0, 0)

Question 5: Explain the process of swapping and negating coordinates when reflecting a point over y = -x.

Answer: To reflect a point (x, y) over y = -x, swap the coordinates to (y, x), then negate both to get (-y, -x).

Question 6: If a point is initially at (7, -2), what is its reflection over y = -x? Show your working.

Answer: (-2, -7)

Question 7: A real-world scenario: A drone is flying at coordinates (5, -4). It needs to move to a position that is the reflection over y = -x. What are the new coordinates?

Answer: (-4, -5)

Question 8: Construct a triangle with vertices at (1, 2), (3, -1), and (-2, 4). Reflect it over y = -x and record the new vertices. Then, explain how the swapping and negation process was applied.

Answer: Vertices after reflection: (-2, -1), (-3, -1), (-4, 2). Process: swap x and y, then negate both coordinates for each point.

Question 9: Identify and correct the mistake in this reflection process: Reflect (2, -3) over y = -x by simply negating both coordinates.

Answer: Incorrect because negating both yields (-2, 3), which is not the reflection. Correct method: swap to (-3, 2), then negate to (3, -2).

Question 10: A complex shape is reflected over y = -x. The original shape has vertices at (6, -2), (-4, 5), and (0, 0). List the reflected vertices and describe the overall transformation.

Answer: Reflected vertices: (2, -6), (-5, 4), (0, 0). Transformation: swap coordinates, then negate both for each point.