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The points W(-2,-2), X(-6,2) , Y(2,5) and Z(6,1) are the vertices of parallelogram...

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nhl123 | Student, Grade 11 | Valedictorian

Posted March 20, 2013 at 2:34 AM via web

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The points W(-2,-2), X(-6,2) , Y(2,5) and Z(6,1) are the vertices of parallelogram WXYZ. Show that the diagonals XY and WY bisect each other.

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mariloucortez | High School Teacher | (Level 3) Adjunct Educator

Posted March 20, 2013 at 3:12 AM (Answer #1)

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To show that the diagonals bisect each other. Get the midpoint of the diagonals. If they are the same, then it is proven that they bisect each other. Start with WY. 

The midpoint is solved by: 

`x = (x_1+x_2)/2`

`y=(y_1+y_2)/2`

The points are W(-2,-2) and Y(2,5). Either point can have the subscript 1 or 2. Just be consistent. If you considered 5 as `y_2`

then 2 would be `x_2.`

Considering WY:

`x = (-2 + 2) / 2 = 0`

`y=(-2+5)/2 = 3/5`

So the midpoint of diagonal WY is (0,3/2)

Consider XZ: X(-6,2) and Z(6,1)

`x=(-6+6)/2=0`

`y=(2+1)/2 = 3/2`

As you can see, the diagonals have the same midpoint. Therefore, you can conclude that they bisect each other.  

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pramodpandey | College Teacher | Valedictorian

Posted March 20, 2013 at 5:23 AM (Answer #2)

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W(-2,-2) ,X(-6,2),Y(2,5) and Z(6,1)

mid point of diagonal WY is `(x_1,y_1)` where

`x_1=(-2+2)/2 ,y_1=(-2+5)/2`

`(x_1,y_1)=(0,3/2)`

Modpoint of diagonal XZ is `(x_2,y_2)`  where

`x_2=(-6+6)/2 ,y_2=(2+1)/2`

`(x_2,y_2)=(0,3/2)` , which is same as mid point of  WY i.e.

This proves that diagonal of parallelogram bisect each other.

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