SOLUTION: Given the coordinates M(-8,-1) A(-2,5) T(3,7) H(-3,1) - Plot the quadrilateral on the plane. - Prove that the quadrilateral is a parallelogram. Use mathmatics to justify you

Algebra ->  Parallelograms -> SOLUTION: Given the coordinates M(-8,-1) A(-2,5) T(3,7) H(-3,1) - Plot the quadrilateral on the plane. - Prove that the quadrilateral is a parallelogram. Use mathmatics to justify you      Log On


   

Question 716743: Given the coordinates
M(-8,-1)
A(-2,5)
T(3,7)
H(-3,1)
- Plot the quadrilateral on the plane.
- Prove that the quadrilateral is a parallelogram. Use mathmatics to justify your answer.
- What special parallelogram is quadrilateral MATH?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Given the coordinates
M(-8,-1)
A(-2,5)
T(3,7)
H(-3,1)
- Plot the quadrilateral on the plane.
-

Prove that the quadrilateral is a parallelogram. Use mathmatics to justify your answer.
Use the slope formula

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

to show that MA ∥ HT

To find the slope of MA

Use (x1,y1) = (-8,-1)
and where (x2,y2) = (-2,5)

m = %28%285%29-%28-1%29%29%2F%28%28-2%29-%28-8%29%29 = %285%2B1%29%2F%28-2%2B8%29 = 6%2F6 = 1

To find the slope of HT

Use (x1,y1) = (-3,1)
and where (x2,y2) = (3,7)

m = %28%287%29-%281%29%29%2F%28%283%29-%28-3%29%29 = %287-1%29%2F%283%2B3%29 = 6%2F6 = 1

So MA ∥ HT because the have the same slope of 1 each.

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Use the slope formula

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

to show that MH ∥ AT


To find the slope of MH

Use (x1,y1) = (-8,-1)
and where (x2,y2) = (-3,1)

m = %28%281%29-%28-1%29%29%2F%28%28-3%29-%28-8%29%29 = %281%2B1%29%2F%28-3%2B8%29 = 2%2F5 

To find the slope of AT

Use (x1,y1) = (-2,5)
and where (x2,y2) = (3,7)

m = %28%287%29-%285%29%29%2F%28%283%29-%28-2%29%29 = %287-5%29%2F%283%2B2%29 = 2%2F5

So MH ∥ AT because the have the same slope of 2%2F5 each.

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- What special parallelogram is quadrilateral MATH?
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