If `R(x , y)` is a point on the line segment joining the points `P(a , b)a n dQ(b , a),` then prove that `x+y=a+b`

Explanation

Given,

`P(a , b) and Q(b , a),`

Let point `R` divides the line joining `P` and `Q` in the ratio `lambda: 1`

then,

`x=(lambdab+a)/(lambda+1)
`and

`y=(lambdaa+b)/(lambda+1)`

So,

`x+y=(lambdaa+b)/(lambda+1) +(lambdab+a)/(lambda+1) `

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