# Question #2ca3e

Mar 8, 2015

First, plot and label all the points in this problem that are of interest on a coordinate system. Then sketch of the lines that form the two quadrilaterals of interest. (This is intended to make it easier to think about the question.)

Find the midpoint of each line segment forming the first quadrilateral, then show that opposite sides connecting the midpoints are parallel (by showing that they have equal slopes).

Mid (EF) = (0,4). Mid (FG) = (6, 2) the line segment joining them has slope $- \frac{1}{3}$
The side opposite the previous line connects Mid(EH) = (-2, -3) and Mid(GH) = (4, -5). The slope of this line is also $- \frac{1}{3}$

The line segment connecting Mid(EF) = (0,4) to Mid (EH) = (-2, -3) has slope $\frac{7}{2}$, as does the segment joining Mid(FG) = (6, 2) to Mid(GH) = (4, -5).

I can't figure out how to put single points or line segments on the graph, so I can't do that part for you.

The midpoint of the line segment from E to F is $\left(\frac{- 5 + 5}{2} , \frac{2 + 6}{2}\right) = \left(0 , 4\right)$.

The midpoint of the line segment from F to G is $\left(\frac{5 + 7}{2} , \frac{6 - 2}{2}\right) = \left(6 , 2\right)$.

The slope of the line through these two midpoints is $\frac{2 - 4}{6 - 0} = \frac{- 2}{6} = \frac{- 1}{3}$.

Now do the same kind of thing for the opposite side, which is the line segment joining the midpoints of EH and GH.

Then do the same thing for the other two side of the second quadrilateral.