If `a ,b ,c` and `u ,v ,w` are the complex numbers representing the vertices of two triangles such that `(c=(1-r)a+r b` and `w=(1-r)u+r v ,` where `r` is a complex number, then the two triangles have the same area (b) are similar are congruent (d) None of these

Options

A. have the same area
B. are similar
C. are congruent
D. Non of these

Answer

B

Explanation

Since a,b,c and u,v ware the vertice of two triangles
Also `c=(1-r) a+ rb `
and `w= (1-r ) u+rb `
Applying `R_3rarr R_3-{(1-r)R_1+rR_2)}`s
`=|{:(" "a" "u" "1),(" "b" "v" "1),(c-(1-r)a-rb w-(1-r)u-rv 1 - (1-r)-r):}|`
`=|(a,u,1),(b,v,1),(0,0,0)|=0 " "[from Eq. (i) ]`