`A B` is a line segment and line `l` is its perpendicular bisector. If a point `P` lies on `l ,` show that `P` is equidistant from `A` and `Bdot`

Explanation

To show that point P is equidistant from points A and B when it lies on the perpendicular bisector of line segment AB, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Elements**:
- Let \( A \) and \( B \) be two points that define the line segment \( AB \).
- Let \( C \) be the midpoint of segment \( AB \).
- Line \( l \) is the perpendicular bisector of segment \( AB \), which means it intersects \( AB \) at point \( C \) at a right angle (90 degrees).
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