Prove that the line y - x + 2 = 0 divides the join of points (3, -1) and (8, 9) in the ratio 2 : 3.
Let AB be the line segmentLet P be any point which divides the line segment in the ratio 2 : 3 then using section formulax=lx2+mx1l+m,y=ly2+my1l+mwhere l:m::2:3⇒ x=2(8)+3(3)2+3=16+95=255=5y=2(9)+3(−1)2+3=18−35=155=3Now P must lie on the line, where p is (5, 3)y−x+2=0⇒ 3−(5)+2=0−2+2=00=0Hence proved.