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.
- 15/2 ( 2/15 ) = - 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 QM: ( - 12,- 11), ( - 14,4)
sqrt(( - 14-( - 12))^2+( 4-( - 11))^2)
sqrt(229)
Length of MN: ( - 14,4), ( 1, 6)
sqrt(( 1-( - 14))^2+( 6- 4)^2)
sqrt(229)
Length of NP: ( 1, 6), ( 3, - 9)
sqrt(( 3- 1)^2+( - 9- 6)^2)
sqrt(229)
Length of PQ: ( 3, - 9), ( - 12,- 11)
sqrt(( - 12- 3)^2+( - 11-( - 9))^2)
sqrt(229)
Our parallelogram has four congruent sides. Therefore, the most precise name for this quadrilateral is square.
