Complex Numbers And Quadratic Equations question 341
Question: The points $ 1+3i,5+i $ and $ 3+2i $ in the complex plane are [MP PET 1987]
Options:
A) Vertices of a right angled triangle
B) Collinear
C) Vertices of an obtuse angled triangle
D) Vertices of an equilateral triangle
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ z_1=1+3i,z_2=5+i $ and $ z_3=3+2i $ Then area of triangle $ A=\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} 1 & 3 & 1 \\ 5 & 1 & 1 \\ 3 & 2 & 1 \\ \end{vmatrix} =0 $ Hence $ z_1,z_2 $ and $ z_3 $ are collinear.
BETA
