Question

Show that the following points taken in order form the vertices of a rhombus.

(1, 0), (5, 3), (2, 7) and ( - 2, 4)

Answer 1

A rhombus have all the lines equal. AB=BC=CD=DA

AB= rad [(1-5)^2+(0-3)^2]
AB= rad [(-4)^2+(-3)^2]
AB= rad 16+9
AB= rad 25
AB=5

BC= rad [(5-2)^2+(3-7)^2]
BC= rad [3^2+(-4)^2]
BC= rad 9+16
BC= rad 25
BC=5

CD= rad [(2-(-2))^2+(7-4)^2]
CD= rad [(2+2)^2+(-3)^2]
CD= rad (4^2+9)
CD= rad 16+9
CD= rad 25
CD=5

DA=rad [(-2-1)^2+(4-0)^2]
DA= rad [(-3)^2+(4)^2]
DA= rad 25
DA=5

SO, AB=BC=CD=DA=5 => ABCD rhombus