Let us show that the points (2, 5), (5, 9), (9, 12) and (6, 8) form a rhombus when they are joined orderly.
Let
A = (2, 5)
B = (5, 9)
C = (9, 12)
D = (6, 8)
Distance between two points = ![]()
AB =
= ![]()
BC =
= 5
CD =
= ![]()
DA =
= ![]()
Since all the sides are equal, the polygon qualifies as a rhombus.
The rhombus formed will look like:

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