Question

Let $A(h,k),B(1,1)$ and $C(2,1)$ be the vertices of a right angled triangle with $AC$ as its hypotenuse. If the area of the triangle is 1 square unit, then the set of values which ${}^{\prime }{k}^{\prime }$ can take is given by

• A. {$-1,3$}
• B. {$-3,-2$}
• C. {$1,3$}
• D. {$0,2$}

Answer 1

The correct option is A {$-1,3$}

Given : The vertices of a right angled triangle $A(1,k),B(1,1)$ and $C(2,1)$ and Area of $\Delta ABC$ = 1 square unit


We know that, area of right angled triangle
$=\frac{1}{2}\times BC\times AB=1\frac{1}{2}\left(1\right)|(k-1)|\Rightarrow \pm (k-1)=2\Rightarrow k=-1,3$