How can you determine if a parallelogram on a coordinate grid is a rhombus

A parallelogram, is just a four-sided polygon, quadrilateral, with two pairs of parallel sides.

a rhombus is a parallelogram, namely the left and right sides are parallel and the top and bottom sides are also parallel to each other.

however, what we call a rhombus, is really a parallelogram that has sides that are all equal in length, besides being parallel.

so on a grid or wherever else, if you have a parallelogram that has four sides that are all equal in length, then is also a rhombus.