SOLUTION: Quadrilateral ABCD has vertices A(-3,1), B(1,4), C(4,0), and D(0,-3). Prove that quadrilateral ABCD is a square.

Algebra ->  Geometry-proofs -> SOLUTION: Quadrilateral ABCD has vertices A(-3,1), B(1,4), C(4,0), and D(0,-3). Prove that quadrilateral ABCD is a square.       Log On


   

Question 1173693: Quadrilateral ABCD has vertices A(-3,1), B(1,4), C(4,0), and D(0,-3). Prove that quadrilateral ABCD is a square.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Check the distances for each of the sides
distance = sqrt (distance of x^2+distance of y^2)
AB has distance sqrt (25) or 5
BC has distance 5
CD the same
DA the same
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Then prove that adjacent sides have slopes that are negative reciprocals of each other, so are perpendicular.
AB (3/4)
BC (-4/3)
CD (3/4)
DA (-4/3)
Equal sides perpendicular to each other. This is a square.