Show that points`A (a , b + c)`, `B (b , c + a)`, `C (c , a + b)`are collinear.

Explanation

We have given the points as `A(a,b+c), B(b,c+a), C(c,a+b)`

Then we have to show that they are collinear.

As we know that the points are called collinear points if the area of triangle is zero.

So , if the points `(x_1,y_1), (x_2,y_2), (x_3,y_3)` are collinear then :

`[x_1(y_2−y_3)+x_2(y_3−y_1)+x_3(y_1−y_2)]=0`

`[a(c+a−a−b)+b(a+b−b−c)+c(b+c−c−a)]=0`

`[ac−ab+ab−bc+bc−ac]=0`

Hence it shows that the points `A(a,b+c), B(b,c+a), C(c,a+b)`are collinear.