determine whether parallelogram jklm with vertices j(-7, -2), k(0, 4), l(9, 2) and m(2, -4) is a rhombus, square, rectangle or all three.

a. rhombus

b. square

c. rectangle

d. rhombus, square and rectangle

To determine the type of parallelogram evaluate the distance between the corners using distance formula, d = quare root of  [(x2−x1)^2+(y2−y1)^2]. For rhombus and square, sides JK = KL = LM = MN. Another, if only two pairs of sides are identical it is either rectangle or parallelogram. If diagonal lines between opposite corners are equal (JL = KM), it is either square or rectangle. For the example: sides JK = KL = LM = MN = 85 and diagonal lines JL =  272 KM = 68. Therefore, this is a rhombus.