Question

The name of the figure formed by the points $(0,0,0),(1,0,1)$ and $(0,1,1)$ is

• A. a straight line
• B. an isosceles triangle
• C. an equilateral triangle
• D. a scalene triangle

Answer 1

Answer: (C)

an equilateral triangle

The distance between the points $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ is $\sqrt{(x_1-x_2{)}^2+(y_1-y_2{)}^2+(z_1-z_2{)}^2}$.

The distance between the origin and $(x_1,y_1,z_1)$ is $\sqrt{x_1^2+y_1^2+z_1^2}$.

lets take A $(1,0,1)$ and B$(0,1,1)$
and there is origin $O(0,0,0)$
length of line segment $AO=\sqrt{2}=BO$
length of line segment $AB=\sqrt{1+1+0}=\sqrt{2}$
since $AO=BO=AB⟹$ All sides are equal $⟹$ equilateral triangle