Question

The triangle formed by the points (0, 7, 10), (–1, 6, 6),(– 4, 9, 6) is [RPET 2001]

• A. Equilateral
• B. Isosceles
• C. Right angled
• D. Right angled Isosceles

Answer 1

The correct option is D

Right angled Isosceles

Let A be (0, 7, 10), B (–1, 6, 6) and C (– 4, 9, 6)
Then, AB = $\sqrt{1+1+16}=\sqrt{18}=3\sqrt{2}$
BC = $\sqrt{9+9+0}=\sqrt{18}=3\sqrt{2}$
AC = $\sqrt{16+4+16}=\sqrt{36}=6$
Clearly, $A{C}^2=A{B}^2+B{C}^2$
Hence $△$ is right angled. Also, since AB = BC
$\therefore △$ is right angled isosceles.