Question

Prove that A (b+a, c), B( C+ a, b)
and C (c+b, a)
are collinear​

Answer 1

Answer:

Step-by-step explanation:

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 , y ), (x , y ) and (x , y ) are collinear

then [x (y - y ) + x ( y - y )+ x (y - y )] = 0. ⇒ [ a( c + a - a - b) + b( a + b - b - c) + c( b + c - c - a) ] = 0 ⇒ [ ac - ab + ab - bc + bc - ac ] = 0 = 0.

∴ the points (a,b+c), (b,c+a), (c,a+b) are collinear.