Answer: The quadrilateral is not a parallelogram.
Explanation:
Slope of any line = (Change in y)/(Change in x)
Slope of LM = (9-6)/(5-(-1)) = 3/6 = 1/2
Slope of LN = (2-6)/(0-(-1)) = -4/1 = -4
Slope of LP = (-2-6)/(-8-(-1)) = -8/-7 = 8/7
Slope of MN = (2-9)/(0-5) = -7/-5 = 7/5
Slope of MP = (-2-9)/(-8-5) = -11/-13 = 11/13
Slope of NP = (-2-2)/(-8-0) = -4/-8 = 1/2
Since slopes of LM and NP are the same, they are parallel lines.
Parallelograms have two sets of parallel lines. However, there only exists one set of parallel lines for this quadrilateral. Thus, this quadrilateral is not a parallelogram.