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)

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