Question 716743
Given the coordinates 
M(-8,-1)
A(-2,5)
T(3,7)
H(-3,1)
- Plot the quadrilateral on the plane.
-
<pre>
{{{drawing(600,480,-10,5,-3,9, grid(1),
circle(-8,-1,.1), locate(-8,-1,"M(-8,-1)"),
circle(-2,5,.1), locate(-2,5,"A(-2,5)"),
circle(3,7,.1), locate(3,7,"T(3,7)"),
circle(-3,1,.1), locate(-3,1,"H(-3,1)"),
green(line(-8,-1,-2,5),line(-2,5,3,7),line(3,7,-3,1),line(-3,1,-8,-1))

)}}}
</pre>
Prove that the quadrilateral is a parallelogram. Use mathmatics to justify your answer.
<pre>
Use the slope formula

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

to show that MA &#8741; HT

To find the slope of MA

Use (x<sub>1</sub>,y<sub>1</sub>) = (-8,-1)
and where (x<sub>2</sub>,y<sub>2</sub>) = (-2,5)

m = {{{((5)-(-1))/((-2)-(-8))}}} = {{{(5+1)/(-2+8)}}} = {{{6/6}}} = 1

To find the slope of HT

Use (x<sub>1</sub>,y<sub>1</sub>) = (-3,1)
and where (x<sub>2</sub>,y<sub>2</sub>) = (3,7)

m = {{{((7)-(1))/((3)-(-3))}}} = {{{(7-1)/(3+3)}}} = {{{6/6}}} = 1

So MA &#8741; HT because the have the same slope of 1 each.

--------------

Use the slope formula

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

to show that MH &#8741; AT


To find the slope of MH

Use (x<sub>1</sub>,y<sub>1</sub>) = (-8,-1)
and where (x<sub>2</sub>,y<sub>2</sub>) = (-3,1)

m = {{{((1)-(-1))/((-3)-(-8))}}} = {{{(1+1)/(-3+8)}}} = {{{2/5}}} 

To find the slope of AT

Use (x<sub>1</sub>,y<sub>1</sub>) = (-2,5)
and where (x<sub>2</sub>,y<sub>2</sub>) = (3,7)

m = {{{((7)-(5))/((3)-(-2))}}} = {{{(7-5)/(3+2)}}} = {{{2/5}}}

So MH &#8741; AT because the have the same slope of {{{2/5}}} each.

----------------------------------------------------- 
</pre>
- What special parallelogram is quadrilateral MATH?
<pre>
This parallelogram is neither a rhombus nor a rectangle, so
there is nothing special about this parallelogram other
than the fact that its coordinates spell "MATH", and math
happens to be the name of the subject you are studying.  :)

Edwin</pre>