If points R (x,y) lies on …
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Posted by Reet Brar 6 years, 6 months ago
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Sia ? 6 years, 6 months ago
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} : 1.
{tex}\therefore x = \frac { \lambda b + a } { \lambda + 1 }{/tex}
{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.
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