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

Since R(*x*, *y*) is a point on the line segment joining the point, P(*a*, *b*) and Q(*b*, *a*).

∴ P(*a*, *b*), Q(*b*, *a*) and R(*x*, *y*)are the collinear.

⇒ Area of ΔPQR = 0

**Area of triangle whose vertices are (****x**_{1}**, ****y**_{1}**), (****x**_{2}**, ****y**_{2}**) and (****x**_{3}**, ****y**_{3}**) .**

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