The slopes are not equal, FJ and GH are not parallel, and FGHJ is not a parallelogram.
To show that quadrilateral FGHJ is a trapezoid, we need to show that it has one pair of parallel sides. We can find the slopes of the two sides FG and HJ and check if they are equal.
The slope of FG is (2-2.1)/(2-3.2) = -0.7/-1.2 = 7/12
The slope of HJ is (1-(-1))/4-(-3) = 2/7
Since the slopes are not equal, FG and HJ are not parallel, and FGHJ is a trapezoid.
To show that FGHJ is not a parallelogram, we need to show that it does not have two pairs of parallel sides. We have already shown that FG and HJ are not parallel. We can also find the slopes of sides FJ and GH and check if they are equal.
The slope of FJ is (2-(-1))/(3.2-(-3)) = 3.3/6.2 = 33/62
The slope of GH is (1-2)/(4-2) = -1/2
Since the slopes are not equal, FJ and GH are not parallel, and FGHJ is not a parallelogram.