Find the equation of the straight line which divide the join of the points (2,3) and (-5,8) in the ratio 3:4 and is also perpendicular to it.

Explanation

To find the equation of the straight line that divides the line segment joining the points (2, 3) and (-5, 8) in the ratio 3:4 and is also perpendicular to it, we can follow these steps:

### Step 1: Find the coordinates of the point that divides the segment in the ratio 3:4.

Using the section formula, the coordinates of the point \( C(x, y) \) that divides the line segment joining points \( A(2, 3) \) and \( B(-5, 8) \) in the ratio \( m:n = 3:4 \) are given by:

\[
C(x, y) = \left( \frac{m \cdot x_2 + n \cdot x_1}{m+n}, \frac{m \cdot y_2 + n \cdot y_1}{m+n} \right)
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