SOLUTION: SOLUTION: Find by calculating gradient whether or not the opposite sides of quadrilateral ABCD are parallel. A is (2,1), B is (14,9);C is (24,23), D is (10,13

Algebra ->  Expressions -> SOLUTION: SOLUTION: Find by calculating gradient whether or not the opposite sides of quadrilateral ABCD are parallel. A is (2,1), B is (14,9);C is (24,23), D is (10,13      Log On


   

Question 903967: SOLUTION: Find by calculating gradient whether or not the opposite sides of quadrilateral ABCD are parallel. A is (2,1), B is (14,9);C is (24,23), D is (10,13
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Let's draw it and see.



It does look like a parallelogram, but looks can fool you!

Find the gradient (slope) of AB

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
where (x1,y1) = (2,1)
and where (x2,y2) = (14,9)

m = %289-1%29%2F%2814-2%29
m = 8%2F12
m = 2%2F3


Find the gradient (slope) of CD

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
where (x1,y1) = (24,23)
and where (x2,y2) = (10,13)

m = %2813-23%29%2F%2810-24%29
m = %28-10%29%2F%28-14%29
m = 5%2F7

Oh! oh! AB and CD are NOT parallel!

Find the gradient (slope) of AD

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
where (x1,y1) = (2,1)
and where (x2,y2) = (10,13)

m = %2813-1%29%2F%2810-2%29
m = 12%2F8
m = 3%2F2

Find the gradient (slope) of BC

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
where (x1,y1) = (14,9)
and where (x2,y2) = (24,23)

m = %2823-9%29%2F%2824-14%29
m = 14%2F10
m = 7%2F5


Oh! oh! AD and BC are NOT parallel either!!!

So neither pair of opposite sides a parallel.

Told you looks can deceive you!!  :)

Edwin