Question

Let $ A(a, 0) $ , $ B(0, b) $ and $ C (1, 1) $ be three points. If $ \frac{1}{a}+\frac{1}{b}=1 $ , then the three points are

• A. vertices of an equilateral triangle
• B. vertices of a right angled triangle
• C. collinear
• D. vertices of an isosceles triangle

Answer 1

Answer: (C)

Area of $\Delta ABC = \begin{vmatrix}a&0&1\\ 0&b&1\\ 1&1&1\end{vmatrix} $
$ = a\left(b-1\right) -0 + 1\left(0-b\right) $
$ = ab - a -b = 0$
$ \left[\because \frac{1}{a} +\frac{1}{b} = 1 \Rightarrow b + a = ab\right]$
$\therefore $ Points $A, B$ and $C$ are collinear.