Q5 of 35 Page 787

Show that the points A(1, 1, 1), B(-2, 4, 1), C(1, -5, 5) and D(2, 2, 5) are the vertices of a square.

To prove: Points A, B, C, D form square.


Formula:


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


D=


Here,


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


(x2,y2,z2)= (-2, 4, 1)


(x3,y3,z3)= (-1, 5, 5)


(x4,y4,z4)= (2, 2, 5)


Length AB =


=


=


=


=


Length BC =


=


=


=


=


Length CD =


=


=


=


=


Length AD =


=


=


=


=


Length AC =


=


=


=


=


Length BD =


=


=


=


=


Here, AB = BC = CD = AD


Also, AC = BD


This means all the sides are the same and diagonals are also equal.


Hence vertices A, B, C, D form a square.


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