Question 1: What are the new coordinates of the point (3, 7) after reflection across the line y=x?

Answer: (7, 3)

Question 2: Reflect the point (-5, 2) across the line y=x. Write the reflected coordinates.

Answer: (2, -5)

Question 3: Plot the point (4, -3) and its reflection across y=x on the grid.

Answer: ( -3, 4 )

Question 4: If a point has coordinates (x, y), what are its coordinates after reflection across y=x?

Answer: The coordinates become (y, x).

Question 5: A point has coordinates (8, -2). Reflect it across y=x and then plot both points on the grid.

Answer: ( -2, 8 )

Question 6: Explain why swapping the coordinates of a point reflects it across the line y=x.

Answer: Swapping the coordinates exchanges the x and y values, which is equivalent to reflecting the point across the line y=x because the line y=x is the set of points where x=y.

Question 7: Construct a triangle with vertices at (1, 2), (3, 4), and (5, 0). Reflect each vertex across y=x and label both the original and reflected vertices on the grid.

Answer: Vertices after reflection: (2, 1), (4, 3), (0, 5).

Question 8: A point is at (-6, 9). What are the coordinates after reflection, and what does this tell you about the symmetry of the line y=x?

Answer: (9, -6); the line y=x is the line of symmetry for points and their reflections.

Question 9: Identify and correct the mistake: A student says that reflecting (2, 3) across y=x gives (2, 3). Is this correct? Explain.

Answer: No, the reflection swaps the coordinates, so (2, 3) reflected across y=x is (3, 2).

Question 10: Challenge: Given a point (x, y), derive a general formula for its reflection across y=x and verify it with the point (7, -4).

Answer: Reflected point is (y, x). For (7, -4), reflection is (-4, 7).