Question

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

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

Answer 1

Answer: (D)

Right angled Isosceles

Answer 2

Let A be (0, 7, 10), B (–1, 6, 6) and C (– 4, 9, 6)

Then, $A B = \sqrt { 1 + 1 + 16 } = \sqrt { 18 } = 3 \sqrt { 2 }$

$B C = \sqrt { 9 + 9 + 0 } = \sqrt { 18 } = 3 \sqrt { 2 }$

$A C = \sqrt { 16 + 4 + 16 } = \sqrt { 36 } = 6$

Clearly, $A C ^ { 2 } = A B ^ { 2 } + B C ^ { 2 }$

Hence $\Delta$ is right angled. Also, since $A B = B C$

∴ $\Delta$ is right angled isosceles.