Question

If $A\equiv (3,4),B\equiv (-3,2)$ and $C\equiv (-5,-4)$, then which of the following statements is correct?

• A. $ABC$ forms a right angled triangle.
• B. $ABC$ forms an acute angled triangle.
• C. $ABC$ forms an obtuse angled triangle.
• D. $ABC$ does not form a triangle.

Answer 1

The correct option is C $ABC$ forms an obtuse angled triangle.

Given : $A\equiv (3,4),B\equiv (-3,2),C\equiv (-5,-4)$
$AB=\sqrt{36+4}=2\sqrt{10}$ units
$BC=\sqrt{4+36}=2\sqrt{10}$ units
$AC=\sqrt{64+64}=8\sqrt{2}$ units
Checking the condition for formation of a triangle,
$AB+BC>ACAB+AC>BCAC+BC>AB$
So, it forms a triangle.

Now, $A{C}^2=128,A{B}^2=40,B{C}^2=40$
$A{C}^2>A{B}^2+B{C}^2$
Hence, $ABC$ is an obtuse angled triangle.