SOLUTION: Prove quadrilateral LOVE is a rhombus but not a square. L (2,2) O (-1,1) V (-2,-2) E (1,-1)

Algebra ->  Geometry-proofs -> SOLUTION: Prove quadrilateral LOVE is a rhombus but not a square. L (2,2) O (-1,1) V (-2,-2) E (1,-1)      Log On


   

Question 1033853: Prove quadrilateral LOVE is a rhombus but not a square.
L (2,2) O (-1,1) V (-2,-2) E (1,-1)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Quadrilateral LOVE is a parallelogram, with sides LO and VE having slope 1/3 and sides OV and LE having slope 3.
Also, abs%28OL%29+=+sqrt%2810%29+=+abs%28OV%29 after using the distance formula.
It is enough to show that one of the interior angles is not a right angle.
Angle OVE theta is evaluated as follows:
==> theta+=+tan%5E-1%284%2F3%29+%3C%3Epi%2F2.
Therefore LOVE is a rhombus but not a square.