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

The correct option is A Isosceles and right angled

Let vertices be $A(4,0);B(-1,-1);C(3,5)$

Slope of $AB=\frac{-1}{-5}=\frac{1}{5}$; slope of $BC=\frac{6}{4}=\frac{3}{2}$

$CA=\frac{5}{-1}=-5$

$\therefore AB\perp CA$

$AB=\sqrt{5^2+1^2}=\sqrt{26};BC=\sqrt{4^2+6^2}=\sqrt{52}$

$CA=\sqrt{1^2+5^2}=\sqrt{26}$

$\therefore$Right angles isosceles (A)