Math help???? Coordinate geometry?

Question

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

Answer 1

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.