Question

The points $1 + 3i,5 + i$ and $3 + 2i$ in the complex plane are

• A. Vertices of a right angled triangle
• B. Collinear
• C. Vertices of an obtuse angled triangle
• D. Vertices of an equilateral triangle

Answer 1

Answer: (B)

Collinear

Answer 2

Sol. Let $z_{1} = 1 + 3i,z_{2} = 5 + i$ and $z_{3} = 3 + 2i$. Then area of triangle $A = \frac{1}{2}\left| \begin{matrix} x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & y_{3} & 1 \end{matrix} \right|$ $= \frac{1}{2}\left| \begin{matrix} 1 & 3 & 1 \\ 5 & 1 & 1 \\ 3 & 2 & 1 \end{matrix} \right| = 0$, Hence $z_{1},z_{2}$ and $z_{3}$ are collinear.