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 triangleI 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

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

1.	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 triangleI 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» 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.

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