Question

A triangle with vertices $ (4,\,0),\,(-1,\,-1),\,(3,\,5) $ is:

• A. isosceles and right angled
• B. isosceles but not right angled
• C. right angled but not isosceles
• D. neither right angled nor isosceles

Answer 1

Answer: (A)

$A B=\sqrt{(4+1)^{2}+(0+1)^{2}}=\sqrt{26} $
$B C=\sqrt{(3+1)^{2}+(5+1)^{2}}=\sqrt{52}$
$C A=\sqrt{(4-3)^{2}+(0-5)^{2}}=\sqrt{26} $
So, in isosceles triangles side $A B=C A$
For right angled triangle
$B C^{2}=A B^{2}+A C^{2}$
So, here $B C=\sqrt{52}=B C^{2}=52$
or $(\sqrt{26})^{2}=(\sqrt{26})^{2}=52$
So, given vertices is right angled and also is isosceles triangle.