Question

Prove that the points (a, b + c), (b, c + a) and (c, a + b) are collinear.

Answer 1

Concept:
Application:

Let $\Delta$ be the area of the triangle formed by the points (a, b+c), (b, c+a) and (c, a+b).

We have,

$\therefore \Delta =\frac{1}{2}|a(c+a)+b(a+b)+c(b+c)-b(b+c)+c(c+a)+a(a+b)|$

$\Rightarrow \Delta =\frac{1}{2}|(ac+a^2+ab+b^2+bc+c^2)-(b^2+bc+c^2+ca+a^2+ab)|$

$\Rightarrow \Delta =0$

Hence, the given points are collinear.