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)

Isosceles and right angled

Answer 2

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

$AB = \sqrt{26},AC = \sqrt{26}$, $BC = \sqrt{52}$; i.e. $AB = AC$

So triangle is isosceles and also $(BC)^{2} = (AB)^{2} + (AC)^{2}$. Hence $\Delta$ABC is right angled isosceles triangle