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Math help???? Coordinate geometry?

+1 vote
Use the distance formula to show that quad.
XYZW is a parallelogram

Coordiantes are

X. -3,5
Y. 2,7
Z. 4,3
W. 1,1

Show that this quad is a parallelogram
asked Jan 10, 2013 in GEOMETRY by mathgirl Apprentice

1 Answer

+1 vote

Parallelogram is xy = wz and xw = yz.

In a Parallelogram opposite sides are equal.

Check whether the lengths of xy = wz and xw = yz. are equal.

Distance formula : points A(x₁, y₁)B(x₂, y₂) distance is √[( x₂ - x₁ )2+( y₂ - y₁ )2]

x (-3, 5) and y (2, 7) then xy = √[ ( 2 - (-3) )2+( 7 - 5 )2 ]

xy = √[52 + 22]

xy = √[25 +4 ]

There fore xy = √[29 ]

w (1, 1) z (4, 3) then wz = √[ ( 4 - 1 )2+( 3 - 1 )2 ]

wz = √[ ( 3 )2+( 2 )2 ]

wz = √[ 9 + 4 ]

wz = √13

xy is not equal to wz

x (-3, 5) w (1, 1) then xw = √[ ( 1 - (-3) )2+( 1 - 5 )2 ]

xw = √[ ( 1 + 3) )2+( - 4 )2 ]

xw = √[ ( 4 )2+( 16 ) ]

xw = √[ (16) + (16)]

xw = √( 32 )

y = (2, 7) z(4, 3) then yz = √[ ( 4 - 2 )2+( 3 - 7 )2 ]

yz = √[ (2)2 + (-4)2 ]

yz = √[ 4 + 16 ]

yz = √[ 20 ]

xw is not equal to yz

Since xy = wz and xw = yz. are not equal, with the given vertices it will not form a parallelogram.

answered Jan 23, 2013 by richardson Scholar

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