**Answer with explanation:**

The four vertices of a two dimensional geometrical shape are set of points A(–1, 2), B(5, 2),C (5, –4), and D(–1, –4).

Now plotting it on X Y plane

Point of intersection of Diagonals that is AC and B D given by the formula

Distance formula between two points in two dimensional plane

**So, the Quadrilateral is Rhombus,because all sides are equal.**

Slope of line between two points is given by

Slope of AB

Slope of BC

Product of slopes = -1

Hence ∠ABC=90°

If in a rhombus one angle measures 90°,then it a Square.

**So, Above Quadrilateral with given vertices is a Square.**