Question 1: Reflect the point (3, -5) across the line y = -x. Write the coordinates of the reflected point.

Answer: (-5, -3)

Question 2: Reflect the point (-2, 4) over y = -x. What are the new coordinates?

Answer: (4, 2)

Question 3: If a point has coordinates (x, y), what are the coordinates after reflection across y = -x?

Answer: (y, x)

Question 4: Plot the point (2, -3) on the grid. Reflect it across y = -x and label the new point.

Answer: (-3, -2)

Question 5: A triangle has vertices at (1, 2), (3, -4), and (-2, -1). Reflect each vertex across y = -x and list their new coordinates.

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

Question 6: A point moves from (5, -3) to (-3, 5) after reflection. Is this the correct reflection across y = -x? Explain your reasoning.

Answer: Yes, because reflection over y = -x swaps and negates the coordinates, so (x, y) becomes (-y, -x).

Question 7: Construct a triangle with vertices at (2, 3), (4, -1), and (-3, -2). Reflect the triangle across y = -x. What are the new vertices?

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

Question 8: Identify and correct the mistake in this reflection: A student reflected (6, -2) to (-6, 2), claiming this is y = -x reflection.

Answer: This is correct; reflection over y = -x swaps and negates x and y coordinates, so (6, -2) correctly becomes (-2, -6). The student's answer is incorrect; they got the order or signs wrong.

Question 9: Given the point (-7, 3), perform a reflection across y = -x manually. Show your working and the final coordinates.

Answer: (-3, 7)

Question 10: Challenge: Find all points on the line y = x that are mapped onto the points on the line y = -x after reflection. Explain your reasoning.

Answer: Points on y = x, when reflected over y = -x, become points on y = -x. The points that are fixed (mapped onto themselves) satisfy y = -x = x, so y = x and y = -x intersect only at (0,0). Thus, only (0,0) is fixed.