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If a ,b ,c and u ,v ,w are the complex n...

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 (a)have the same area (b) are similar (c)are congruent (d) None of these

A

have the same area

B

are similar

C

are congruent

D

Non of these

Text Solution

Verified by Experts

The correct Answer is:
B
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) ]`
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