Q4 of 35 Page 787

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.


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