Consider a line segment \(AB\).
Let \(P\) be any point on the line segment which divides it into two unequal parts in the ratio \(m : n\)
Let \(A\) be \(x_1\), \(P\) be \(x\) and \(B\) be \(x_2\) such that \(x_2 > x > x_1\).
The co-ordinate of \(P\) divides the line segment in the ratio \(m : n\).
This means, .
\(n(x - x_1)\) \(=\) \(m(x_2 - x)\)
\(nx - nx_1 = mx_2 - mx\)
\(mx + nx = mx_2 + nx_1\)
\(x(m + n) = mx_2 + nx_1\)
If \(A\), \(P\), and \(B\) has the coordinates \((x_1\), \(y_1)\), \((x\), \(y)\), and \((x_2\), \(y_2)\) respectively, then: