Question

If $R(x,y)$ is a point on the line segment joining the points $P(a,b)andQ(b,a)$, then prove that $x+y=a+b$.

Answer 1

$P(a,b)$ and $Q(b,a)$ and $R(x,y)$ lies on $\stackrel{⟷}{PQ}\stackrel{⟷}{PQ}=(y-b)=\frac{a-b}{b-a}(x-a)=>y-b=-x+a=>y+x=a+b$

as $R(x,y)$ lies on it, proven