Show that each quadrilateral with the given vertices is a parallelogram. J(-2,-2), K(-3,3), L(1,5), M(2,0)

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  J +L = K +M = (-1, 3)

Step-by-step explanation:

The figure JKLM is a parallelogram if the midpoints of the diagonals are the same point. That is, ...

  (J +L)/2 = (K +M)/2

Multiplying by 2 makes this a simpler test:

  J +L = K +M

In this quadrilateral, those sums are ...

  J +L = (-2, -2) +(1, 5) = (-2+1, -2+5) = (-1, 3)

  K +M = (-3, 3) +(2, 0) = (-3+2, 3+0) = (-1, 3)

The midpoints are the same, so the quadrilateral is a parallelogram.