SOLUTION: quadrilateral abcd has vertices a(-3 2) b(-1 5) c(5 1) and d(3 -2). prove that abcd is a rectangle

Algebra ->  Geometry-proofs -> SOLUTION: quadrilateral abcd has vertices a(-3 2) b(-1 5) c(5 1) and d(3 -2). prove that abcd is a rectangle      Log On


   

Question 1021050: quadrilateral abcd has vertices a(-3 2) b(-1 5) c(5 1) and d(3 -2). prove that abcd is a rectangle
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Line AB has slope m%5BAB%5D+=+%285-2%29%2F%28-1%2B3%29+=+3%2F2
Line CD has slope m%5BCD%5D+=+%281%2B2%29%2F%285-3%29+=+3%2F2
==> Lines AB and CD are parallel.
Line BC has slope m%5BBC%5D+=+%285-1%29%2F%28-1-5%29+=+-2%2F3
Line AD has slope m%5BAD%5D+=+%282%2B2%29%2F%28-3-3%29+=+-2%2F3
==> Lines BC and AD are parallel.
Last thing is to just show that one of the four angles is a right angle.
Since the slope of line AB, 3/2, and the slope of line CD, -2/3, have a product of -1, it follows that the angle at vertex C is a right angle, and the proof is complete.