Question 1127887: [Quadrilateral] If the oppisite sides of a quadrilateral are use parallel, then it is a parallelogram. Use slopes to determine wheather the points (-6,1),(-2,-1),(0,3), and (4,1) are the vertices of a parallelogram.
Found 2 solutions by josmiceli, MathLover1:
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! A( -6,1 )
B( -2,-1 )
C( 0,3 )
D( 4,1 )
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slope AB = ( 1 -(-1) ) / ( -6 -(-2) )
slope AB = 2/(-4)
slope AB = -1/2
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slope BC = ( 3 -(-1) ) / ( 0 -(-2) )
slope BC = 4/2
slope BC = 2
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slope AC = ( 3 - 1 ) / ( 0 -(-6)
slope AC = 2/6
slope AC = 1/3
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slope BD = ( 1 -(-1) ) / ( 4 -(-2) )
slope BD = 2/6
slope BD = 1/3
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slope AD = ( 1 - 1 ) / ( 4 -(-6)
slope AD = 0
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slope CD = ( 1 - 3 ) / ( 4 - 0 )
slope CD = -2 / 4
slope CD = -1/2
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There are 1 pair of parallel lines with slope = -1/2
Also, there are 1 pair of parallel lines with slope = 1/3
So it is a parallelogram, and the lines BC and AD
must be the diagonals
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website!
( , ),( , ),( , ), and ( ,)
(,),(,)->the oppisite sides of a quadrilateral are use parallel
(0,3), (4,1)
since slopes are same, lines passing through points above are parallel
(,),(,) other the oppisite sides of a quadrilateral are use parallel
(-2,-1),(4,1)
since slopes are same, lines passing through points above are parallel
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