Show that the points A(1, -1, -5), b(3, 1,3) and C(9, 1, -3) are the vertices of an equilateral triangle.
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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