Question

Which segment is the image of Line segment A B reflected across the line y = negative 2?

On a coordinate plane, segment A B goes from (2, negative 7) to (8, negative 3), segment J K goes from (2, 7) to (8, 3), segment G H goes from (2, 3) to (8, negative 1), segment F A goes from (negative 4, negative 3) to (2, negative 7), and C D goes from (negative 8, negative 3) to (negative 2, negative 7).
Line segment A F
Line segment D C
Line segment G H
Line segment J K

Answer 1

To find the image of line segment AB reflected across the line \( y = -2 \), we first determine the coordinates of the endpoints A (2, -7) and B (8, -3).

1. **Reflecting point A (2, -7)**:
- The line \( y = -2 \) is horizontal, and the distance from point A to the line \( y = -2 \) can be calculated as follows:
- Distance from A to line: \( -7 - (-2) = -7 + 2 = -5 \).
- Therefore, point A reflects to \( -5 \) units above the line \( y = -2 \):
- Reflected A = \( -2 + 5 = 3 \).
- Hence, A' = (2, 3).

2. **Reflecting point B (8, -3)**:
- Similar to point A, the distance from B to the line:
- Distance from B to line: \( -3 - (-2) = -3 + 2 = -1 \).
- The point will reflect 1 unit above the line \( y = -2 \):
- Reflected B = \( -2 + 1 = -1 \).
- Hence, B' = (8, -1).

Now we have the reflected points A' (2, 3) and B' (8, -1). The line segment A'B' is the reflection of the original segment AB across the line \( y = -2 \).

Now, we compare this result with the segments given:
- Segment JK: from (2, 7) to (8, 3)
- Segment GH: from (2, 3) to (8, -1)

The only matching segment with one end point as (2, 3) and the other as (8, -1) is **segment GH**.

Therefore, the correct answer is: **Line segment GH**.