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