+91-87964 74404
FlagBACK
Question icon
Grade Upto college level Algebra

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

Profile image of Manvendra Singh chahar
12 Years agoGrade Upto college level
Answers icon

1 Answer

Profile image of SHAIK AASIF AHAMED
12 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

Other Related Questions on algebra

question mark
What is a binomial expression?
algebra
1 Answer Available

Last Activity: 2 Years ago

question mark
Can we divide two vectors? If this is possible then how?
algebra
1 Answer Available

Last Activity: 2 Years ago

question mark
How do you write “the product of 18 and q” as an algebraic expression?
algebra
1 Answer Available

Last Activity: 2 Years ago

question mark
दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे
algebra
1 Answer Available

Last Activity: 3 Years ago

question mark
Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely. why HCF and not LCM as “least” keywor dis given?
algebra
1 Answer Available

Last Activity: 3 Years ago