Question 1: Reflect the point (-4, 7) across the x-axis. What are the new coordinates?

Answer: (-4, -7)

Question 2: Plot the point (3, -5) on the grid. Then reflect it across the x-axis and write the reflected coordinates.

Answer: (3, 5)

Question 3: A character in a video game is located at (6, -2). When the game reflects the character's position across the x-axis, what are the new coordinates?

Answer: (6, 2)

Question 4: Describe the process of reflecting a point (x, y) across the x-axis. Write the general formula.

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

Question 5: A drone is at position (x, y) = (10, -8). It performs a reflection across the x-axis. Write the coordinates after reflection.

Answer: (10, 8)

Question 6: In a gaming simulation, the position of an object is at (–7, 4). After reflecting across the x-axis, what are the coordinates? Plot both points on the grid.

Answer: (–7, –4)

Question 7: A robot moves from (2, 3) to its reflected position across the x-axis. Calculate the new position and explain the change.

Answer: The new position is (2, -3). The y-coordinate sign is flipped due to reflection across the x-axis.

Question 8: Construct a point with coordinates (–5, 6). Reflect it across the x-axis and verify the reflection by plotting both points.

Answer: (–5, –6)

Question 9: A gaming character is at position (4, -7). During a mirror effect, the position is reflected across the x-axis. What is the new position? Show your working.

Answer: (4, 7)

Question 10: Identify the common mistake students make when reflecting points across the x-axis and suggest how to correct it.

Answer: A common mistake is reversing the sign of the x-coordinate instead of the y-coordinate. To correct this, remember that reflection across the x-axis only changes the y-coordinate to its negative.

Question 11: A virtual object in a 2D game is at (–3, 9). After reflecting across the x-axis, what are its new coordinates? Plot the original and reflected points on the grid.

Answer: (–3, –9)

Question 12: Challenge: The position of an item is at (x, y). It undergoes two reflections: first across the y-axis, then across the x-axis. Write an expression for the final coordinates in terms of x and y, and confirm the result when x=3 and y=–4.

Answer: First reflection across y-axis: (–x, y). Then across x-axis: (–x, –y). For x=3, y=–4, final coordinates are (–3, 4).