Question 1: Reflect the point A(3, 5) across the x-axis. Write down the coordinates of A' after reflection.

Answer: 3, -5

Question 2: A point B is at (−4, 2). Reflect B across the x-axis. What are the new coordinates?

Answer: −4, -2

Question 3: Plot the point (−1, 3) on the grid. Reflect it across the x-axis and label the new point.

Answer: −1, -3

Question 4: If a point P has coordinates (x, y), what are the coordinates of its reflection P' across the x-axis?

Answer: x, -y

Question 5: A triangle has vertices at (2, 4), (5, 1), and (3, 3). Reflect the triangle across the x-axis. Write the new coordinates of each vertex.

Answer: 2, -4; 5, -1; 3, -3

Question 6: A real-world scenario: A drone is flying at position (6, 8). It then reflects its position across the x-axis to avoid obstacles. What are the new coordinates?

Answer: 6, -8

Question 7: Construct a rectangle on the grid with vertices at (1, 2), (4, 2), (4, 5), and (1, 5). Reflect the rectangle across the x-axis and list the new vertices.

Answer: 1, -2; 4, -2; 4, -5; 1, -5

Question 8: A point C is at (−3, −7). What are its coordinates after reflection across the x-axis? Explain your reasoning.

Answer: The y-coordinate changes sign, so C' is at (−3, 7).

Question 9: A reflection across the x-axis is performed on the point (x, y). If the reflected point is at (x, −y), find the coordinates of the original point given the reflected point (−2, −5).

Answer: −2, 5

Question 10: Identify and correct the mistake in the following student's work: The student reflected the point (4, -3) across the x-axis and wrote the new point as (4, 3).

Answer: The reflection across the x-axis changes the sign of the y-coordinate; so the correct point is (4, -3). The student's answer (4, 3) is incorrect because they did not change the y-coordinate sign.

Question 11: Find the images of the points (−5, 0), (0, 0), and (3, -4) after reflection across the x-axis. Write down all three coordinates.

Answer: −5, 0; 0, 0; 3, 4