Question 554928
<pre>
Plot the points and draw the figure MATH:

 M(5,4), A(3,-6), T(0,-10), H(2,0). 

{{{drawing(200,400,-2,6,-11,5,
graph(200,400,-2,6,-11,5),green(line(2,0,0,-10),line(5,4,3,-6)),
red(line(2,0,5,4), line(3,-6,0,-10)), locate(2.8,4.5,"M(5,4)"),
locate(3,-6,"A(3,-6)"), locate(.2,-10,"T(0,-10)"), locate(.2,.7,"H(2,0)"),
 
circle(5,4,.1), circle(3,-6,.1), circle(0,-10,.1), circle(2,0,.1)  )}}}

Lines are parallel if they have the same slope.  A parallelogram is
a quadrilateral with both pairs of oposite sides parallel.

So we use the slope formula on all four sides.

m = {{{(y[2]-y[1])/(x[2]-x[1])}}}

Slope of MA:   M (5,4), A (3,-6), 

m = {{{((-6)-(4))/((3)-(5))}}} = {{{(-10)/-2}}} = 5

Slope of TH:   T(0,-10), and H(2,0). 

m = {{{((0)-(-10))/((2)-(0))}}} = {{{10/2}}} = 5

So one pair of sides are parallel since both have slope 5.

Slope of MH:    M(5,4), H(2,0).

m = {{{((0)-(4))/((2)-(5))}}} = {{{(-4)/(-3)}}} = {{{4/3}}}

Slope of AT:    A(3,-6), T(0,-10),

m = {{{((-10)-(-6))/((0)-(3))}}} = {{{(-10+6)/(-3)}}} = {{{(-4)/(-3)}}} = {{{4/3}}}
 
So the other pair of sides are also parallel since both have slope {{{4/3}}}.

So MATH is a parallelogram.

Edwin</pre>