Question 1: Reflect the point (3, 5) across the y-axis. What are the new coordinates?

Answer: (-3, 5)

Question 2: Reflect the point (-2, -7) across the y-axis. Write down the reflected coordinates.

Answer: (2, -7)

Question 3: A point P at (4, -3) is reflected across the y-axis. What are the coordinates of P'?

Answer: (-4, -3)

Question 4: Plot the point (2, -4) and its reflection across the y-axis on the grid. What are the coordinates of the reflected point?

Answer: (-2, -4)

Question 5: Construct the reflection of the point (-6, 2) across the y-axis. Record the new coordinates.

Answer: (6, 2)

Question 6: A triangle has vertices at (1, 2), (4, 5), and (1, 8). Reflect this triangle across the y-axis and list the new coordinates of each vertex.

Answer: {"A'":"(-1, 2)","B'":"(-4, 5)","C'":"(-1, 8)"}

Question 7: A square has vertices at (3, 1), (3, 4), (6, 4), and (6, 1). Reflect the square across the y-axis. What are the new vertex coordinates?

Answer: {"A'":"(-3, 1)","B'":"(-3, 4)","C'":"(-6, 4)","D'":"(-6, 1)"}

Question 8: A point is at (x, y) and after reflection it is at (-x, y). If the original point was at (x, y), express x in terms of the reflection.

Answer: The original x-coordinate is x; reflection changes it to -x.

Question 9: A robot at position (7, -2) moves to its reflection across the y-axis. What is its new position? Explain the steps involved.

Answer: The robot moves from (7, -2) to (-7, -2) by reflecting across the y-axis, which changes the x-coordinate sign.

Question 10: If a point (x, y) is reflected across the y-axis to (-x, y), find the error if someone mistakenly writes the reflected point as (x, -y). Identify and correct the mistake.

Answer: The mistake is reflecting across the x-axis instead of the y-axis. Correct reflection yields (-x, y).

Question 11: Challenge: The point (x, y) is reflected across the y-axis. The resulting point is (-x, y). If another point is reflected across the x-axis, what would be its coordinates? Provide your reasoning.

Answer: Reflected across x-axis: (x, -y).

Question 12: A real-world scenario: A drone flying at (3, 5) needs to perform a reflection across the y-axis for a mirrored delivery route. What are the new coordinates, and why is this reflection useful?

Answer: New coordinates: (-3, 5). Reflection helps in planning the route for the mirrored delivery path across the vertical axis for symmetric coverage.