Question

You are given the coordinates of four points that are the vertices of a parallelogram. You need to determine if the parallelogram is a rhombus. Explain how you could determine this.

Answer 1

A rhombus is a parallelogram, namely, is a polygon with four sides and two pairs of parallel sides.

the one distinction of a rhombus with other parallelograms is that, a rhombus has all equal sides, all its four sides are the same length, so, if you already know the vertices are for a parallelogram, then is a given two pairs of sides are parallel.

so...  you simply need to check their length, making sure they're all equal, using the distance formula.