Question

Prove that the line y - x + 2 = 0 divides the join of points (3, -1) and (8, 9) in the ratio 2 : 3.

Answer 1

$\text{Let AB be the line segment}\text{Let P be any point which divides the line segment in the ratio 2 : 3 then using section formula}x=\frac{l{x}_2+m{x}_1}{l+m},y=\frac{l{y}_2+m{y}_1}{l+m}wherel:m::2:3\Rightarrow x=\frac{2\left(8\right)+3\left(3\right)}{2+3}=\frac{16+9}{5}=\frac{25}{5}=5y=\frac{2\left(9\right)+3(-1)}{2+3}=\frac{18-3}{5}=\frac{15}{5}=3\text{Now P must lie on the line, where p is (5, 3)}y-x+2=0\Rightarrow 3-\left(5\right)+2=0-2+2=00=0\text{Hence proved.}$