Show that the points A(a,b+c), B(b,c+a) and C(c,a+b) are collinear.
Attachments:
Answers
Answered by
5
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.
please mark me brainlist
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.
please mark me brainlist
Similar questions