Question

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.

Answer 1

as we know that 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 (x1, y1), (x2, y2) and (x3, y3) .

a(a-y)+b(y-b)+x(b-a)=0

-ay+by+bx-xa=b^2-a^2

(x+y)(b-a)=(b-a)(b-a)

x+y=b-a

Hope it helps you.