Question 1197664
<pre>
I'll do all but the last two steps.

{{{drawing(400,400,-2,11,-4,9,

graph(400,400,-2,11,-4,8),

line(3,5,9,7), line(9,7,8,-2), line(8,-2,4,-1), line(4,-1,3,5),

locate(2,5.5,"(3,5)"), locate(9,7.6,"(9,7)"), locate(8,-2,"(8,-2)"),
locate(2.6,-1,"(4,-1)")

 )}}}

We use the midpoint formula to find the midpoints of the sides:

Midpoint = {{{(matrix(1,3,(x[1]+x[2])/2, ",",(y[1]+y[2])/2))}}} 

Midpoint of the top side:

Midpoint = {{{(matrix(1,3,(3+9)/2, ",",(5+7)/2))}}} =
           {{{(matrix(1,3,12/2, ",",12/2))}}}
           {{{(matrix(1,3,6, ",",6))}}}

Midpoint of the left side:

Midpoint = {{{(matrix(1,3,(3+4)/2, ",",(5+(-1))/2))}}} =
           {{{(matrix(1,3,7/2, ",",4/2))}}}
           {{{(matrix(1,3,3.5, ",",2))}}}

Midpoint of the bottom side:

Midpoint = {{{(matrix(1,3,(4+8)/2, ",",(-1+(-2))/2))}}} =
           {{{(matrix(1,3,12/2, ",",-3/2))}}}
           {{{(matrix(1,3,6, ",",-1.5))}}}

Midpoint of the right side:

Midpoint = {{{(matrix(1,3,(8+9)/2, ",",(-2+7)/2))}}} =
           {{{(matrix(1,3,17/2, ",",5/2))}}}
           {{{(matrix(1,3,8.5, ",",2.5))}}}

{{{drawing(400,400,-2,11,-4,9,

green(line(6,6,3.5,2),line(6,-1.5,3.5,2),line(6,-1.5,8.5,2.5),line(6,6,8.5,2.5)), 



graph(400,400,-2,11,-4,8),

line(3,5,9,7), line(9,7,8,-2), line(8,-2,4,-1), line(4,-1,3,5),

locate(6,6,"(6,6)"), locate(3.5,2,"(3.5,2)"), locate(4.3,-1.5,"(6,-1.5)"),
locate(8.5,2.5,"(8.5,2.5)")

 )}}}

Now we just need to show that the two pairs of opposite sides are parallel
by showing that the pairs have the same slope.

We use the slope formula:

{{{m}}}{{{""=""}}}{{{(y[2]-y[1])/(x[2]-x[1])}}}
where (x<sub>1</sub>,y<sub>1</sub>) = (6,6)
and where (x<sub>2</sub>,y<sub>2</sub>) = (3.5,2)
{{{m}}}{{{""=""}}}{{{(6-2)/(6-3.5)}}}
{{{m}}}{{{""=""}}}{{{4/(2.5)}}}{{{""=""}}}{{{1.6)}}}

We find the slope of its opposite side

{{{m}}}{{{""=""}}}{{{(y[2]-y[1])/(x[2]-x[1])}}}
where (x<sub>1</sub>,y<sub>1</sub>) = (6,-1.5)
and where (x<sub>2</sub>,y<sub>2</sub>) = (8.5,2.5)
{{{m}}}{{{""=""}}}{{{(2.5-(-1.5))/(8.5-6)}}}
{{{m}}}{{{""=""}}}{{{(2.5+1.5)/2.5}}}
{{{m}}}{{{""=""}}}{{{(4)/(2.5)}}}{{{""=""}}}{{{1.6)}}}

So that shows that those two green sides are parallel,
since their slopes are both 1.6.

I'm going to stop here and let you finish on your own by
showing that the slopes of the other pair of opposite sides 
are also parallel, by showing that they have the same slope 
also, by the same method.

The problem will not be complete until you do this last part.

Edwin</pre>