Given the set of vertices: Q(–2, –1), R(–1, 2), S(4, 1), T(3, –2), the quadrilateral is a rhombus.

To determine if the given quadrilateral is a rhombus, we need to check if all sides are of equal length.

The formula to calculate the distance between two points (x1, y1) and (x2, y2) is √[(x2 - x1)² + (y2 - y1)²].

Let's calculate the lengths of the sides:

1. QR: √[(-1 - (-2))² + (2 - (-1))²] = √[1² + 3²] = √[1 + 9] = √10
2. RS: √[(4 - (-1))² + (1 - 2)²] = √[5² + (-1)²] = √[25 + 1] = √26
3. ST: √[(3 - 4)² + (-2 - 1)²] = √[(-1)² + (-3)²] = √[1 + 9] = √10
4. TQ: √[(-2 - 3)² + (-1 - (-2))²] = √[(-5)² + 1²] = √[25 + 1] = √26

Since all sides are not of equal length (QR = ST ≠ RS = TQ), the given quadrilateral is not a rhombus.