Given the coordinates of the vertices of a quadrilateral, determine whether it is a square, a rectangle, or a parallelogram. then find the perimeter of the quadrilateral.
a(-3, -2), b(2, -2), c(4, 2), d(-1, 2)
a. parallelogram; (10 + 4ö5) units
b. rectangle; (25 + 2ö5) units
c. square; (5 + 2ö5) units
d. none of these

  a.  parallelogram; (10 + 4√5) units

Step-by-step explanation:

The distance formula is ...

  d = √((x2 -x1)² +(y2 -y1)²)

The length AB is ...

  AB = √((2-(-3))² +(-2-(-2))²) = 5

The length BC is ...

  BC = √((4-2)² +(2-(-2))²) = √(4+16) = 2√5

The length of the perimeter of this parallelogram is twice the sum of these:

  P = 2(5+2√5) = 10 +4√5

Lines AB and CD are horizontal, but lines BC and AD are not vertical, so the figure is not a rectangle. It is a parallelogram.