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

MCQ

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

A
Vertices of a right angled triangle
✓
Collinear
C
Vertices of an obtuse angled triangle
D
Vertices of an equilateral triangle

✓

Answer

Correct option: B.

Collinear

b
(b) Let ${z_1} = 1 + 3i,{z_2} = 5 + i$ and ${z_3} = 3 + 2i$
Then area of triangle
$A = \frac{1}{2}\left| {\begin{array}{*{20}{c}}{{x_1}}&{{y_1}}&1\\{{x_2}}&{{y_2}}&1\\{{x_3}}&{{y_3}}&1\end{array}} \right| = \frac{1}{2}\left| {\begin{array}{*{20}{c}}1&3&1\\5&1&1\\3&2&1\end{array}} \right| = 0$
Hence ${z_1},{z_2}$ and ${z_3}$ are collinear.

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