The triangle formed by the points (0, 7, 10), (-1, 6, 6), (-4, 9,… - Vidyadip

MCQ

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

A
Equilateral
B
Isosceles
C
Right angled
✓
Right angled Isosceles

✓

Answer

Correct option: D.

Right angled Isosceles

d
(d) 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 $\Delta $ is right angled. Also, since $AB = BC$

$\Delta $ is right angled isosceles.

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