Question

Jared is given the line segment AB shown below?

A: (-6, -5)
B: (4, 3)

He reflects AB across the y-axis. Then, he reflects the resulting image across the line x = 3. Which translation is equivalent to this double reflection?

A) Translation along the x-axis
B) Translation along the y-axis
C) Translation along the line x = -3
D) Translation along the line y = -3

Answer 1

The double reflection of line segment AB across the y-axis and then the line x = 3 is equivalent to Translation C) along the line x = -3, shifting the segment 6 units to the right along the x-axis.

Step-by-step explanation:

The student asked about the equivalent translation to a double reflection of a line segment AB with points A: (-6, -5) and B: (4, 3) first across the y-axis and then across the line x = 3. To find the equivalent translation, we follow two reflections:

1. Reflecting across the y-axis changes the sign of the x-coordinates, so A becomes (6, -5) and B becomes (-4, 3).
2. Reflecting across the line x = 3 effectively means taking each point's x-coordinate, subtracting 3, and then reversing the sign (because it's reflected). So A becomes (3-(6-3)), which simplifies to 0, and B becomes (3-(-4-3)), which simplifies to 10. Thus, A' is at (0, -5) and B' is at (10, 3).

By comparing the original and final coordinates of A and B, we can see that the entire line segment has moved to the right by 6 units along the x-axis. This is equivalent to Translation C) along the line x = -3.