Question 1: What are the swapped coordinates of the point (3, 7) when reflecting over y=x?

Answer: 7,3

Question 2: If a point has coordinates (−4, 2) and is reflected over y=x, what is its new position?

Answer: 2,−4

Question 3: Calculate the swapped coordinates of the point (−6, −9).

Answer: −9,−6

Question 4: A triangle has vertices at (2, 5), (−3, 4), and (1, −2). Plot the reflected points over y=x and list their new coordinates.

Answer: 5,2; 4,−3; −2,1

Question 5: Identify and correct the mistake in this student’s reflection of point (8, −3): they wrote the new point as (−3, 8). Is this correct? Why or why not?

Answer: Yes, swapping coordinates over y=x results in (−3, 8), so the student is correct.

Question 6: Construct a point on the grid that would be incorrectly reflected if the student swapped the coordinates but forgot to swap the signs of the original point.

Answer: Any point where the swap alone does not produce the correct reflection, e.g., original (−2, 4), incorrect reflection (4, −2), but correct reflection is (4, −2); identify the mistake.

Question 7: A point is initially at (0, 0). After reflection over y=x, where is it located? Explain why.

Answer: (0, 0), because reflecting the origin over y=x leaves it unchanged.

Question 8: If the original coordinate is (−1, 10), what is the reflected coordinate over y=x?

Answer: 10,−1

Question 9: A student claims that reflecting over y=x involves changing the signs of both coordinates. Is this true? Justify your answer.

Answer: No, reflection over y=x involves swapping the coordinates, not changing signs.

Question 10: Challenge: Given the point (x, y), write the algebraic expression for its reflection over y=x.

Answer: The reflected point is (y, x).