SOLUTION: Is quadrilated ABCD with the given verticles A(1,2) B(2,5) C(5,7) D(4,4) a parallelogram?

Algebra ->  Parallelograms -> SOLUTION: Is quadrilated ABCD with the given verticles A(1,2) B(2,5) C(5,7) D(4,4) a parallelogram?       Log On


   

Question 787151: Is quadrilated ABCD with the given verticles A(1,2) B(2,5) C(5,7) D(4,4) a parallelogram?
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Using the gradient formula:
y2 - y1/ x2 - x1
The gradient of AB =
5 - 2/2 - 1
= 3
The gradient of DC =
7 - 4/5 - 4
= 3
The gradient of AD =
4 - 2/4 - 1
= 2/3
The gradient of BC =
7 - 5/5 - 2
= 2/3
As the gradients of AB = DC
and AD = BC
then quadrilateral ABCD
is a parallelogram.
Hope this helps.
:-)