Question

A triangle having vertices as $A(4,4),B(3,5)$ and $C(-1,-1)$ will be

• A. Right angled at $A$
• B. Right angled at $B$
• C. Right angled at $C$
• D. Not a right angled triangle

Answer 1

The correct option is A Right angled at $A$

Let $m_1,m_2$ and $m_3$ be the slopes of $AB,AC$ and $BC$ respectively, then
$m_1=$ Slope of line $AB=\frac{5-4}{3-4}=-1$
$m_2=$ Slope of line $AC=\frac{-1-4}{-1-4}=1$
$m_3=$ Slope of line $BC=\frac{-1-5}{-1-3}=\frac{3}{2}$
Clearly we can see that
$m_1{m}_2=-1$
So, it is a right angled triangle having right angle at $A.$