The sides with slope 0 are horizontal, and the sides with an undefined slope are vertical. Therefore, consecutive sides are perpendicular. This means that our quadrilateral is either a rectangle or a square. 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
( - 1,1), ( - 1,6)
sqrt(( - 1-( - 1))^2+( 6- 1)^2)
5
ML
( - 1,6), ( 4,6)
sqrt(( 4-( - 1))^2+( 6- 6)^2)
5
LK
( 4,6), ( 4,1)
sqrt(( 4- 4)^2+( 1- 6)^2)
5
KJ
( 4, 1), ( - 1,1)
sqrt(( - 1- 4)^2+( 1- 1)^2)
5
Our parallelogram has all congruent sides. Therefore, the most precise name for this quadrilateral is square. Moreover, note that a square is also a rectangle and a rhombus.
