If points R (x,y) lies on line segment joining points P(a,b)and (b,a). Then prove that x+y=a+b

If points R (x,y) lies on line segment joining points P(a,b)and (b,a).

1.	If points R (x,y) lies on line segment joining points P(a,b)and (b,a). Then prove that x+y=a+b
Answer» According to the question, R(x, y) is a point on the line segment joining the points P(a, b) and Q(b, a)Let point R(x + y) divides the line joining P(a,b) and Q(b,a) in the ratio {tex}\\lambda{/tex}\xa0: 1.{tex}\\therefore x = \\frac { \\lambda b + a } { \\lambda + 1 }{/tex}\xa0{tex}y = \\frac { \\lambda a + b } { \\lambda + 1 }{/tex}Adding, {tex}x+y=\\frac { \\lambda b + a + \\lambda a + b } { \\lambda + 1 }{/tex}{tex}= \\frac { \\lambda ( a + b ) + 1 \\times ( a + b ) } { \\lambda + 1 }{/tex}{tex}= \\frac { ( \\lambda + 1 ) \\times ( a + b ) } { \\lambda + 1 } = a + b{/tex}{tex}\\Rightarrow x+y=a+b{/tex}Hence Proved.