#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# 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

SHAIK AASIF AHAMED
6 years ago
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