Question

$A(4,4),B(3,5)$ and $C(-1,-1)$ are the vertices of

• A. an equilateral triangle
• B. a right angled triangle
• C. an isosceles triangle
• D. None of these

Answer 1

The correct option is B a right angled triangle

In $\Delta ABC$
$m_1=$ slope of $AB=\frac{5-4}{3-4}=-1$
$m_2=$ slope of $AC=\frac{-1-4}{-1-4}=1$
$m_3=$ slope of $BC=\frac{5+1}{3+1}=\frac{3}{2}$
Clearly, $m_1{m}_2=-1$.
$\therefore AB\perp AC$ ie.,
$\angle CAB=\frac{\pi }{2}$
Hence, the given points are the vertices of a right angled triangle.