Show that the points A(0, 1, 2), B(2, -1, 3) and C(1, -3, 1) are the vertices of an isosceles right-angled 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)= (0, 1, 2)
(x2,y2,z2)= (2, -1, 3)
(x3,y3,z3)= (1, -3, 1)
Length AB =
=
=
=
=
Length BC =
=
=
=
=
Length AC =
=
=
=
=
Also, AB2 + BC2 = 9 + 9 = 18 = AC2
Therefore, points A, B, C forms an isosceles right-angled triangle.