Question

A(p ,o) and B(o, q) line on a straight line. If third point C(2, 2) lies on the
same loue prove that :-+-=1/p+1/q=1/2​

Answer 1

The expression is correct

Step-by-step explanation:

Given that A(p,0) and B(0,q) lie on the straight line and also the point C(2,2) lie on the same line

let the equation of line be :

   $y=mx+c$ ....eq(1) [ the standard equation of the straight line ]

∵ the point A(p,0) lie on the line $y=mx+c$

∴ $=>0=mp+c\\=>m=\frac{-c}{p}$........eq(2)

∵ the point B(0,q) also lie on the line $y=mx+c$

$=>q=o+c\\=>c=q$.........eq(3)

From eq(1) and eq(2) and eq(3) we get

              $=>y=\frac{-q}{p} x+q$

∵ the point C(2,2) also lie on the line

            $=>y=\frac{-q}{p} x+q$

∴ $=>2=\frac{-q}{p} \times2+q\\=>2+\frac{2p}{q} =q\\=>\frac{2}{q} +\frac{2}{p}=1\\ =>\frac{1}{p} +\frac{1}{q} =\frac{1}{2}$hence proved