Question

Show that the point (a,b+c),(b,c+a),(c,a+b) are collinear

Answer 1

Answer:

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.

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 (x1, y1), (x2, y2) and (x3, y3) are collinear then [x1(y2 - y3) + x2( y3 - y1)+ x3(y1 - y2)] = 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.