Let point be A(3, -1) and B(8, 9).
Let the line divide the line joining the points A and B in the ratio m:n at any point C(x, y)
By section formula,
Now, substituting value of x and y in equation x - y - 2 = 0,
\(\frac{8m + 3n}{m + n} - \frac{9m - n}{m + n} - 2\) = 0
\(\frac{8m + 3n-9m + n - 2m - 2n}{m + n} \) = 0
∴ - 3m + 2n = 0
∴ \(\frac{m}n = \frac{2}3\)
∴ m:n = 2:3
Hence,
the line divides the line segment joining A and B in the ratio 2:3 internally.
