Question

Show that the following points form a right angled triangle.

(-11, 13), (-3, -1) and (4, 3)

Answer 1

Given,

$A(-11,13)$ $B(-3,-1)$ $C(4,3)$

$AB=\sqrt{8^2+{14}^2}=\sqrt{260}$, $m_{AB}=\frac{-14}{8}$

$BC=\sqrt{7^2+4^2}=\sqrt{65}$ $m_{BC}=\frac{4}{7}$

$AC=\sqrt{{15}^2+{10}^2}=\sqrt{325}$

$A{B}^2+B{C}^2=A{C}^2$ also $m_{AB}\times m_{BC}=-1$

Hence ,it is a right-angled triangle .

Right angled at $B$