# Show that the poi

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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