Question

Prove that (A, A+B) ; (B, C+A) ; (C, C+B) are collinear?
please solve this problem

Answer 1

hi mate here is ur answer

if the points are collinear then the area of triangle equals to 0

so using the formulae of area of triangle

1/2[x1 ( y2-y1) + x2(y3-y1) + x3 ( y1-y2)]

= 1/2[ a[c+a-(c+b))+b(c+b-(a+b))+c(a+b-(c+a)=0

=[ a(c+a-c+b)+b(c+b-a-b)+c(a+b-c-a)]=0

= [a(a+b)+b(c-a)+c(b-c)]=0

=[a^2+ab+bc-ac+bc-c^2]=0

=a^2-c^2 +bc=0

=(a+c)(a-c)+bc= 0

= bc=0/(a+c)(a-c)

bc= 0

thus points are collinear

hope it helps!!!

Answer 2

Answer:

Step-by-step explanation:

Solve it with help of triangle area.

If the area of triangle is 0 then points are

Collinear.