document.write( "Question 407605: the diagonals of a parallelogram intersect at (1,1). two vertices are located at (-6,4) and (-3,-1). find the coordinates of the other vertices. \n" ); document.write( "

Algebra.Com's Answer #287337 by robertb(5830) $\"\"$ $\"About$

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Since the diagonals of a parallelogram bisect each other, then we can use the midpoint formula in reverse. For the vertex opposite (-6,4), we get:\r
\n" ); document.write( "\n" ); document.write( " $\"1+=+%28x%2B%28-6%29%29%2F2\"$ ==> 2 = x - 6 ==> x = 8,
\n" ); document.write( " $\"1+=+%28y%2B4%29%2F2\"$ ==> 2 = y + 4 ==> y = -2.
\n" ); document.write( "Therefore the vertex opposite (-6,4) is (8, -2).\r
\n" ); document.write( "\n" ); document.write( "For the vertex opposite (-3,-1), we get:\r
\n" ); document.write( "\n" ); document.write( " $\"1+=+%28x%2B%28-3%29%29%2F2\"$ ==> 2 = x - 3 ==> x = 5,
\n" ); document.write( " $\"1+=+%28y%2B%28-1%29%29%2F2\"$ ==> 2 = y - 1 ==> y = 3.
\n" ); document.write( "Therefore the vertex opposite (-3,-1) is (5,3).
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