Question

If A, B, C are represented by 3 + 4i, 5 - 2i , -1 + 16i, then A, B, C are
[RPET 1986]

• A. Collinear
• B. Vertices of equilateral triangle
• C. Vertices of isosceles triangle
• D. Vertices of right angled triangle

Answer 1

The correct option is A Collinear

Given that points are A(3 + 4i), B(5 - 2i) and C(-1 + 16i)

Area of triangle = $\frac{1}{2}\left|\begin{array}{ccc}{x}_1& y_1& 1\\ x_2& y_2& 1\\ x_3& y_3& 1\end{array}\right|=\frac{1}{2}\left|\begin{array}{ccc}3& 4& 1\\ 5& -2& 1\\ -1& 16& 1\end{array}\right|=0$
Hence points are collinear.