Find the value of m, if the points (5,1), (-2,-3) and (8,2m) are collinear.

Explanation

To find the value of \( m \) such that the points \( (5, 1) \), \( (-2, -3) \), and \( (8, 2m) \) are collinear, we can use the concept that the area of the triangle formed by these three points must be zero. The formula for the area of a triangle formed by three points \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) is given by:

\[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]

Setting the area to zero for collinearity, we have:

...