document.write( "Question 52904: The points (5,2), (2,6), and (-8,-3) are three vertices of a parallelogram. Locate and give the coordinates of a fourth vertex. Find all possible solutions. \n" ); document.write( "

Algebra.Com's Answer #35298 by venugopalramana(3286) $\"\"$ $\"About$

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The points A=(5,2), B=(2,6), and C=(-8,-3) are three vertices of a parallelogram. Locate and give the coordinates of a fourth vertex. Find all possible solutions.
\n" ); document.write( "WE USE THEPRINCIPAL THAT DIAGONALS OF A PARALLELOGRAM BISECT EACH OTHER.
\n" ); document.write( "IF ABCD IS THE PARALLELOGRAM AND D IS (H,K) THEN
\n" ); document.write( "MID POINT OF AC = [{(5-8)/2=-3/2},{(2-3)/2=-1/2}]=(-1.5,-0.5)=MID POINT OF BD =
\n" ); document.write( "=[(2+H)/2,(6+K)/2]
\n" ); document.write( "2+H=-1.5*2=-3....H=-5
\n" ); document.write( "6+K=-0.5*2=-1.....K=-7
\n" ); document.write( "D IS (-5,-7)
\n" ); document.write( "IF ACBD IS THE PARALLELOGRAM THEN D IS GIVEN BY
\n" ); document.write( "MIDPOINT OF AB IS = (7/2,8/2)= MID POINT OF CD = H-8/2,K-3/2
\n" ); document.write( "H-8=2*7/2=7.......H=15
\n" ); document.write( "K-3=2*8/2=8..........K=11
\n" ); document.write( "HENCE D IS (15,11) \n" ); document.write( "

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