Show that the points A(4, 6, -5), B(0, 2, 3) and C(-4, -4, -1) from the vertices of an isosceles triangle.
To prove: Points A, B, C form isosceles triangle.
Formula:
The distance between two points (x1,y1,z1) and (x2,y2,z2) is given by
D=
Here,
(x1,y1,z1)= (4, 6, -3)
(x2,y2,z2)= (0, 2, 3)
(x3,y3,z3)= (-4, -4, -1)
Length AB = 
= 
= 
= 
= 
= 2
Length BC = 
= 
= 
= 
= 
= 2
Length AC = 
= 
= 
= 
= 
Here, AB = BC
∴ vertices A, B, C forms an isosceles triangle.
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