Question

On a coordinate plane, line segment A B goes from (negative 4, 3) to (negative 1, 1), segment D C goes from (1, 1) to (4, 3), segment F E goes from (3, 1) to (6, 3), segment H G goes from (negative 4, negative 3) to (negative 1, negative 1), segment I J goes from (negative 4, negative 5) to (negative 1, negative 3).
Which segment is a reflection of segment AB over the line x = 1?


Line segment C D
Line segment E F
Line segment G H
Line segment I J

Answer 1

To determine which segment is a reflection of segment AB over the line \(x = 1\), we first need to find the coordinates of the endpoints of segment AB and then calculate their reflections across the line \(x = 1\).

The endpoints of segment AB are:
- A: \((-4, 3)\)
- B: \((-1, 1)\)

Now, we reflect each point over the line \(x = 1\).

**Reflection of point A (-4, 3)**:
- The distance from point A to the line \(x = 1\) is \(1 - (-4) = 5\).
- Therefore, the reflection will be \(1 + 5 = 6\).
- So, the reflected point A' will be \((6, 3)\).

**Reflection of point B (-1, 1)**:
- The distance from point B to the line \(x = 1\) is \(1 - (-1) = 2\).
- Therefore, the reflection will be \(1 + 2 = 3\).
- So, the reflected point B' will be \((3, 1)\).

The reflected segment A'B' goes from \((6, 3)\) to \((3, 1)\).

Now let's examine the given options:

1. **Line segment CD**: From \((1, 1)\) to \((4, 3)\)
2. **Line segment EF**: From \((3, 1)\) to \((6, 3)\)
3. **Line segment GH**: From \((-4, -3)\) to \((-1, -1)\)
4. **Line segment IJ**: From \((-4, -5)\) to \((-1, -3)\)

The segment that matches the reflected coordinates from segment A to segment B is **Line segment EF**, which runs from \((3, 1)\) to \((6, 3)\).

Therefore, the final answer is:
**Line segment EF**.