A quadrilateral with vertices  A(1,3), B(2,0), C(5,1) and D(4,4) is a

To determine the type of the quadrilateral ABCD with vertices A(1,3), B(2,0), C(5,1) and D(4,4), we need to calculate the distances between the vertices (sides of the quadrilateral) and check for any special properties.

Step 1: Calculate the distances between the vertices

The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula: √[(x2-x1)² + (y2-y1)²].

AB = √[(2-1)² + (0-3)²] = √[1 + 9] = √10 BC = √[(5-2)² + (1-0)²] = √[9 + 1] = √10 CD = √[(4-5)² + (4-1)²] = √[1 + 9] = √10 DA = √[(1-4)² + (3-4)²] = √[9 + 1] = √10

Step 2: Check for special properties

From the above calculations, we can see that all sides (AB, BC, CD, DA) are equal in length (√10).

A quadrilateral with all sides of equal length is a rhombus.

Therefore, the quadrilateral ABCD with vertices A(1,3), B(2,0), C(5,1) and D(4,4) is a rhombus.