Prove that the perpendicular drawn from the point `(4,1)` on the join of`(2,-1)a n d(6,5)` divides it in the ratio `5: 8.`

Explanation

To prove that the perpendicular drawn from the point \( (4, 1) \) on the line segment joining the points \( (2, -1) \) and \( (6, 5) \) divides it in the ratio \( 5:8 \), we will follow these steps:

### Step 1: Find the equation of the line joining the points \( (2, -1) \) and \( (6, 5) \).

The slope \( m \) of the line joining two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
...