If p(x,y) lies between the line joining the point A(a,0) and B(0,b) then show that x/a+y/b=1?

If p(x,y) lies between the line joining the point A(a,0) and B(0,b) th

1.	If p(x,y) lies between the line joining the point A(a,0) and B(0,b) then show that x/a+y/b=1?
Answer» If a point (X,Y) lies on a line joining the points A (x1,y1) and B (x2,y2) the equation of the line is given by{tex}\\frac{y-y_{1}}{x-x_{1}}=\\frac{y_{2}-y_{1}}{x_{2}-x_{1}}{/tex}Point P(x,y) lies on the line joining the points A (a,0) and B (0,b). So{tex}\\frac{y-0}{x-a}=\\frac{b-0}{0-a}{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}\\frac{y}{x-a}=-\\frac{b}{a}{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}a y=-b(x-a){/tex}{tex}\\Rightarrow{/tex}\xa0{tex}a y=-b x+a b{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}a y+b x=a b{/tex}divide both side by ab{tex}\\Rightarrow{/tex}\xa0{tex}\\frac{a y}{a b}+\\frac{b x}{a b}=\\frac{a b}{a b}{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}\\frac{y}{b}+\\frac{x}{a}{/tex}= 1 (proved)