Question

Determine whether the quadrilateral is a parallelogram using the indicated method Midpoint Formula:

F(-2, 4), G (4, 2), H (4, -2), J (-2, -1)

Answer 1

To determine if the quadrilateral is a parallelogram using the midpoint formula, we need to find the midpoints of both pairs of opposite sides and check if they are equal.

The coordinates of the midpoint of FG are:

((−2+4)/2, (4+2)/2) = (1, 3)

The coordinates of the midpoint of HJ are:

((4−2)/2, (−2−1)/2) = (1, −1.5)

The coordinates of the midpoint of FH are:

((-2+4)/2, (4−2)/2) = (1, 1)

The coordinates of the midpoint of GJ are:

((4−2)/2, (2−1)/2) = (1, 0.5)

Since the midpoints of opposite sides are equal, we can conclude that the quadrilateral FGHJ is a parallelogram.