Answer :

To prove: Points A, B, C form equilateral triangle.


Formula:


The distance between two points (x1,y1,z1) and (x2,y2,z2) is given by


D=


Here,


(x1,y1,z1)= (1, -1, -5)


(x2,y2,z2)= (3, 1,3)


(x3,y3,z3)= (9, 1, -3)


Length AB =


=


=


=


= = 6


Length BC =


=


=


=


= = 6


Length AC =


=


=


=


= = 6


Hence, AB = BC = AC


Therefore, Points A, B, C make an equilateral triangle.


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