We can tell that the slopes of the opposite sides of our quadrilateral are equal. Therefore, both pairs of opposite sides are parallel and the quadrilateral is a parallelogram. Additionally, the consecutive sides are perpendicular, as their slopes are opposite reciprocals.
- 2 * 1/2 = -1
Therefore, our parallelogram is either a rectangle or a square. To check, we can find the lengths of its sides using the Distance Formula.
Side
Distance Formula
Simplified
Length of HK: ( - 2,- 3), ( - 3,- 1)
sqrt(( - 3-( - 2))^2+( - 1-( - 3))^2)
sqrt(5)
Length of KJ: ( - 3,- 1), ( 3, 2)
sqrt(( 3-( - 3))^2+( 2-( - 1))^2)
sqrt(45)
Length of JI: ( 3, 2), ( 4, 0)
sqrt(( 4- 3)^2+( 0- 2)^2)
sqrt(5)
Length of IH: ( 4, 0), ( - 2,- 3)
sqrt(( - 2- 4)^2+( - 3- 0)^2)
sqrt(45)
Our parallelogram has two pairs of opposite congruent sides. Therefore, the most precise name for this quadrilateral is rectangle.
