Question

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

Answer 1

The points are A(a,b+c), B(b,c+a), C(c,a+b)

If the area of triangle is zero then the points are called collinear points.

if three points ($x_1,y_1$), ($x_2,y_2$), ($x_3,y_3$) are collinear then :

$\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$=0

$\left[a\right(c+a-a-b)+b(a+b-b-c)+c(b+c-c-a\left)\right]=0$

$[ac-ab+ab-bc+bc-ac]=0$

=0

The points A(a,b+c), B(b,c+a), C(c,a+b) are collinear.