Question

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

Answer 1

a. parallelogram; (10 + 4√5) units

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.