Question

The three points A (7, 0, 10), B (6, -1, 6), C (9, -4, 6) form ________________

(a) equilateral triangle

(b) right angled triangle

(c) isosceles triangle

(d) right angled isosceles triangle

I have been asked this question during an internship interview.

The query is from Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 11

Answer 1

Correct choice is (d) right angled isosceles triangle

Explanation: We know, distance between two points (x1, y1, z1) and (x2, y2, z2) is \(\sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}\).

Distance AB = \(\sqrt{(7-6)^2+(0+1)^2+(10-6)^2} = \sqrt{18}\)

Distance BC = \(\sqrt{(6-9)^2+(-1+4)^2+(6-6)^2} = \sqrt{18}\)

Distance AC = \(\sqrt{(7-9)^2+(0+4)^2+(10-6)^2} = \sqrt{36}\)

Since AB = BC and AB^2+BC^2 = AC^2 so, it forms right angled isosceles triangle.