Question 1: Reflect the point with coordinates (3, -5) across the x-axis. Write the new coordinates.

Answer: 3, 5

Question 2: A point P at (–4, 7) is reflected across the x-axis. What are the coordinates of the reflected point?

Answer: –4, –7

Question 3: Plot the point (2, –3) and its reflection across the x-axis on the grid.

Answer: Plot at (2, –3) and (2, 3).

Question 4: If a point is reflected across the x-axis and ends up at (–6, 2), what was its original position?

Answer: –6, –2

Question 5: A triangle has vertices at (1, 2), (4, 3), and (2, –1). Reflect this triangle across the x-axis. List the new vertices.

Answer: 1, –2; 4, –3; 2, 1

Question 6: Describe the step-by-step process to reflect a point (x, y) across the x-axis. Why does the y-coordinate change sign?

Answer: To reflect (x, y) across the x-axis, change the y-coordinate to its opposite (–y), while x remains the same. This is because reflection across the x-axis flips the point over the x-axis, reversing its vertical position but not its horizontal position.

Question 7: A real-world scenario: A drone starts at (3, 4) and flies such that its position is reflected across the x-axis. What is its new position? How might this affect navigation?

Answer: The drone's new position is at (3, –4). This affects navigation by reversing its vertical coordinate, so any altitude-related instructions need to be adjusted accordingly.

Question 8: A point (x, y) is reflected across the x-axis and then another transformation is applied. If the final coordinates are (x', y'), express y' in terms of the original y.

Answer: y' = –(original y)

Question 9: Identify the common mistake made when reflecting points across the x-axis and explain how to avoid it.

Answer: A common mistake is changing the sign of the x-coordinate instead of the y-coordinate. To avoid this, remember that reflection across the x-axis only affects the y-coordinate, changing its sign, while x remains unchanged.

Question 10: Challenge: Given a point (–2, 5), reflect it across the x-axis twice. What are the resulting coordinates?

Answer: –2, 5

Question 11: Extension: Consider a point (x, y). Write a general formula for its coordinates after reflection across the x-axis, then extend this to reflection across both axes.

Answer: Reflected across x-axis: (x, –y). Across both axes: (–x, –y).