We can tell that consecutive sides are notperpendicular, as their slopes are notopposite reciprocals.
- 2(2/5 ) ≠-1
Therefore, our quadrilateral is either a parallelogram or a rhombus. To check this, we can find the lengths of its sides using the Distance Formula.
Side
Points
d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)
Simplify
JM
( - 2,- 1), ( 3,1)
sqrt(( 3-( - 2))^2+( 1-( -1))^2)
sqrt(29)
ML
( 3,1), ( 1,5)
sqrt(( 1- 3)^2+( 5- 1)^2)
2sqrt(5)
LK
( 1,5), ( - 4, 3)
sqrt(( - 4- 1)^2+( 3- 5)^2)
sqrt(29)
KJ
( - 4, 3), ( - 2,-1)
sqrt(( - 2-( - 4))^2+( - 1- 3)^2)
2sqrt(5)
Our parallelogram has two pairs of congruent sides. Therefore, the most precise name for this quadrilateral is a parallelogram.
