We can tell that consecutive sides are notperpendicular, as their slopes are notopposite reciprocals.
0 (4/3 ) ≠-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
( - 4,- 1), ( - 1,3)
sqrt(( - 1-( - 4))^2+( 3-( -1))^2)
5
ML
( - 1,3), ( 4,3)
sqrt(( 4-( - 1))^2+( 3- 3)^2)
5
LK
( 4,3), ( 1, -1)
sqrt(( 1- 4)^2+( -1- 3)^2)
5
KJ
( 1, -1), ( - 4,-1)
sqrt(( - 4- 1)^2+( - 1-( -1))^2)
5
Our parallelogram has four congruent sides. Therefore, the most precise name for this quadrilateral is a rhombus.
