If line `l_1` intersects another line `l_2` at its mid-point in such a way that the angle between them is `90^@` , then the line _____ is called the _______ of the line ______

Options

A. `l_1`, perpendicular bisector, `l_2`
B. `l_2`, perpendicular bisector, `l_1`
C. `l_1`, `l_2`, perpendicular bisector
D. `l_1`, `l_3`, perpendicular bisector

Answer

To solve the question step by step, we need to analyze the given information and fill in the blanks accordingly.

### Step-by-Step Solution:

1. **Identify the Lines**: We have two lines, `l_1` and `l_2`. The question states that `l_1` intersects `l_2`.

**Hint**: Look at the lines and their relationship as described in the question.

2. **Intersection Point**: The intersection occurs at the midpoint of line `l_2`. This means that `l_1` divides `l_2` into two equal segments.

**Hint**: Remember that the midpoint is the point that divides a line segment into two equal parts.

3. **Angle Between Lines**: The angle between `l_1` and `l_2` is given as `90 degrees`. This indicates that the lines are perpendicular to each other.

**Hint**: Think about the definition of perpendicular lines; they form a right angle (90 degrees) at their intersection.

4. **Definition of the Line**: Since `l_1` intersects `l_2` at its midpoint and forms a right angle, `l_1` is not just any line; it has a specific name in geometry.

**Hint**: Recall the terminology used in geometry for lines that bisect another line at a right angle.

5. **Final Answer**: Therefore, we can fill in the blanks:
- The line `l_1` is called the **perpendicular bisector** of the line `l_2`.

### Complete Answer:
If line `l_1` intersects another line `l_2` at its mid-point in such a way that the angle between them is `90 degrees`, then the line **l_1** is called the **perpendicular bisector** of the line **l_2**.