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If a, b, c and u, v, w are complex numbers representing the vertices of two triangles such that c = (1 - r)a + rb and w = (1 - r)u + rv, where r is a complex number, then the two triangles are A. similar B. congruent C. equal in area D. equal bases

If a, b, c and u, v, w are complex numbers representing the vertices of two triangles such that c = (1 - r)a + rb and w = (1 - r)u + rv, where r is a complex number, then the two triangles are
A. similar B. congruent C. equal in area D. equal bases

Grade:Upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
240-1681_2.1.PNG
we have AB=b-a,AC=c-a=(1-r)a+rb-a=r(b-a)
BC=c-b=(1-r)a+rb-b=(r-1)b-(r-1)a =(r-1)(b-a)
PQ=v-u
PR=w-u=(1-r)u+rv-u=r(v-u)
QR=w-v=(1-r)u+rv-v=(1-r)u+(r-1)v=(r-1)(v-u)
Finally
\frac{AB}{AC}=\frac{1}{\left | r \right |},\frac{PQ}{PR}=\frac{1}{\left | r \right |} and \frac{AB}{BC}=\frac{1}{\left | r-1 \right |},\frac{PQ}{QR}=\frac{1}{\left | r-1 \right |}
\frac{AB}{AC}=\frac{PQ}{PR} and \frac{AB}{BC}=\frac{PQ}{QR}
\frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}
so Triangles ABC and PQR are similar
Thanks and Regards
Shaik Aasif
askIITians Faculty

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