Show that points (a,b+c),(b,c+a),(c,a+b) are collinear
Answers
Answered by
1
I will show u with an example .
Answered by
10
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.
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.
Similar questions