How can you determine if a parallellogram on a coordinate grid is a rhombus?

Answer 1

Since you know that it is a parallelogram (not parallellogram!) you already know that the opposite sides are mutually parallel. All you need to do is to establish that any pair of adjacent sides are of equal length, or equivalently, the squares of these lengths are equal. The squared length of the line AB where A = (p,q) and B = (r,s) is

(p - r)^2 + (q - s)^2.

Answer 2

To determine if a parallelogram on a coordinate grid is a rhombus, you need to check if all its sides are congruent. Find the lengths of all four sides using the distance formula and compare them. If all the side lengths are equal, then the parallelogram is a rhombus.