SOLUTION: Quadrilateral NORA has vertices N(3,2) O(7,0), R(11,2) an A(7,4). Use coordinate geometry to prove that quadrilateral NORA is a rhombus.

Algebra ->  Geometry-proofs -> SOLUTION: Quadrilateral NORA has vertices N(3,2) O(7,0), R(11,2) an A(7,4). Use coordinate geometry to prove that quadrilateral NORA is a rhombus.      Log On


   

Question 535938: Quadrilateral NORA has vertices N(3,2) O(7,0), R(11,2) an A(7,4). Use coordinate geometry to prove that quadrilateral NORA is a rhombus.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Quadrilateral NORA has vertices N(3,2) O(7,0), R(11,2) an A(7,4). Use coordinate geometry to prove that quadrilateral NORA is a rhombus.

We prove that all 4 sides are the same length, using the distance formula:
d = sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29
NO = sqrt%28%287-3%29%5E2%2B%280-2%29%5E2%29 = sqrt%284%5E2%2B%28-2%29%5E2%29 = sqrt%2816%2B4%29 = sqrt%2820%29 = sqrt%284%2A5%29 = 2sqrt%285%29
OR = sqrt%28%282-0%29%5E2%2B%2811-7%29%5E2%29 = sqrt%282%5E2%2B4%5E2%29 = sqrt%284%2B16%29 = sqrt%2820%29 = sqrt%284%2A5%29 = 2sqrt%285%29
RA = sqrt%28%287-11%29%5E2%2B%284-2%29%5E2%29 = sqrt%28%28-4%29%5E2%2B2%5E2%29 = sqrt%2816%2B4%29 = sqrt%2820%29 = sqrt%284%2A5%29 = 2sqrt%285%29
AN = sqrt%28%287-3%29%5E2%2B%284-2%29%5E2%29 = sqrt%284%5E2%2B2%5E2%29 = sqrt%2816%2B4%29 = sqrt%2820%29 = sqrt%284%2A5%29 = 2sqrt%285%29
All four sides are of equal length 2sqrt%285%29
Edwin