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For coordinate geometry,if A(2,0),B(p,-2),C(-1,1) and D(3,r) are the vertices of a...

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phanpal999 | Student, Grade 8 | (Level 1) Salutatorian

Posted April 13, 2013 at 3:01 AM via web

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For coordinate geometry,if A(2,0),B(p,-2),C(-1,1) and D(3,r) are the vertices of a parallelogram ABCD,calculate the value of p and of r.

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted April 13, 2013 at 6:40 AM (Answer #1)

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In a parallelogram diagonal bisect each other.Using this result we can calculate p and r .

A(2,0) ,B(p,-2),C(-1,1) and D(3,r)

Mid point of AC =`((2-1)/2,(0+1)/2)`

`=(1/2,1/2)`              (i)

Mid point of BD=`((p+3)/2,(r-3)/2)`        (ii)

from (i) and (ii)

`(1/2,1/2)=((p+3)/2,(r-3)/2)`

`1/2=(p+3)/2 => 1=p+3 => p=1-3`

`p=-2`

and

`1/2=(r-3)/2 => 1=r-3 =>r=1+3`

`r=4`

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