If P (9a-2,-b) divides line segment joining A (3a+1,-3) and B(8a,5) in the ratio `3 : 1`, then find the values of a and b.

Explanation

To solve the problem, we need to find the values of \( a \) and \( b \) given that point \( P(9a-2, -b) \) divides the line segment joining points \( A(3a+1, -3) \) and \( B(8a, 5) \) in the ratio \( 3:1 \).

### Step 1: Use the Section Formula for the x-coordinates

According to the section formula, if a point \( P(x, y) \) divides the line segment joining points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in the ratio \( m:n \), then the coordinates of point \( P \) can be calculated as follows:

\[
x = \frac{mx_2 + nx_1}{m+n}
...