Question 1: Swap the coordinates of the point (3, 7). What are the new coordinates?

Answer: (7, 3)

Question 2: If a point is at (−4, 2), what are its coordinates after swapping?

Answer: (2, -4)

Question 3: Plot the point (5, -3) on the grid and then swap the coordinates. What is the new point?

Answer: (−3, 5)

Question 4: A triangle has vertices at (1, 4), (3, 6), and (5, 2). Swap the coordinates of each vertex. List the new vertices.

Answer: ["(4, 1)","(6, 3)","(2, 5)"]

Question 5: A point (−2, 8) is reflected across the line y=x. What are its new coordinates?

Answer: (8, -2)

Question 6: Construct a triangle with vertices at (−1, 3), (2, 5), and (4, 1). Swap all vertices and draw the new triangle on the grid.

Answer: ["(3, -1)","(5, 2)","(1, 4)"]

Question 7: If a point (x, y) swaps to (y, x), what is the original point if the swapped point is (−6, 9)?

Answer: (9, -6)

Question 8: Explain why swapping the coordinates of a point is equivalent to reflecting it across the line y=x.

Answer: Swapping coordinates (x, y) to (y, x) results in a mirror image across the line y=x because it exchanges the x and y positions, which is the defining property of reflection across y=x.

Question 9: Plot point (4, −7) and swap its coordinates. What are the new coordinates? Then describe the transformation.

Answer: (−7, 4)

Question 10: Two points are at (−3, 5) and (2, −4). Swap their coordinates and determine the new points. Are the points symmetric with respect to y=x?

Answer: ["(5, -3)","(-4, 2)"]

Question 11: Identify and correct the mistake in this process: a student swaps (6, 2) to (6, 2) instead of (2, 6). What is the correct swapped point?

Answer: (2, 6)