If the coordinates of two points `A` and `B` are (3, 4) and `(5,-2)` , respectively, find the coordinates of any point `P` if `P A=P Bdot` Area of ` P A B` is 10 sq. units.

Explanation

To solve the problem, we need to find the coordinates of point \( P \) such that the distance from \( P \) to point \( A \) is equal to the distance from \( P \) to point \( B \), and the area of triangle \( PAB \) is 10 square units.

### Step-by-Step Solution:

1. **Identify the coordinates of points A and B**:
- Point \( A \) has coordinates \( (3, 4) \).
- Point \( B \) has coordinates \( (5, -2) \).

...