Answer :

To prove: Points P, Q, R, S forms rhombus.


Formula:


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


D=


Here,


(x1,y1,z1)= (1, 3, 4)


(x2,y2,z2)= (-1, 6, 10)


(x3,y3,z3)= (-7, 4, 7)


(x4,y4,z4)= (-5, 1, 1)


Length PQ =


=


=


=


=


Length QR =


=


=


=


=


Length RS =


=


=


=


=


Length PS =


=


=


=


=


Length PR =


=


=


=


=


Length QS =


=


=


=


=


Here, PQ = RS =QR = PS .


Also the diagonals PR ≠ QS.


Hence, the polygon is a rhombus as all sides are equal and diagonals are not equal.


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