Complex Numbers And Quadratic Equations question 344
Question: If A, B, C are represented by $ 3+4i, $ $ 5-2i $ , $ -1+16i $ , then A, B, C are [RPET 1986]
Options:
A) Collinear
B) Vertices of equilateral triangle
C) Vertices of isosceles triangle
D) Vertices of right angled triangle
Show Answer
Answer:
Correct Answer: A
Solution:
Given that points are $ A(3+4i),B(5-2i) $ and $ C(-1+16i) $ Area of triangle $ =\frac{1}{2} \begin{vmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \\ \end{vmatrix} =\frac{1}{2} \begin{vmatrix} 3 & 4 & 1 \\ 5 & -2 & 1 \\ -1 & 16 & 1 \\ \end{vmatrix} =0 $ Hence points are collinear.
BETA
