document.write( "Question 1011466: Square QRST has vertices Q(2,8),R(-4,8),S(-4,2),and T(2,2).Triangle QTU shares 2 vertices with square QRST.Whichordered pair describes point U if the area of the triangle QTU is the same as the area of square QRST? \n" ); document.write( "
Algebra.Com's Answer #627127 by KMST(5328)\"\" \"About 
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The square has sides parallel to the x-axis,
\n" ); document.write( "and sides parallel to the y-axis such as \"QT\" on the line \"x=2\" .
\n" ); document.write( "The length of the side of the square
\n" ); document.write( "is the distance
\n" ); document.write( "\"QT=ABS%28y%5BQ%5D-y%5BT%5D%29=abs%288-2%29=6\" .
\n" ); document.write( "If we consider \"QT\" to be the base of square and triangle,
\n" ); document.write( "the area of the square is \"QT%2AQT=QT%2A6\" ,
\n" ); document.write( "and the area of the triangle is
\n" ); document.write( "\"QT%2Aheight%2F2\" .
\n" ); document.write( "We want \"QT%2Aheight%2F2=QT%2A6\"-->\"height%2F2=6\"-->\"height=2%2A6\"-->\"height=12\" .
\n" ); document.write( "So \"U\" is a point at a distance of \"12\" units from line \"x=2\" containing segment base\"QT\" .
\n" ); document.write( "It could be anywhere on line \"x=2%2B12\"<-->\"x=14\" , or
\n" ); document.write( "on line \"x=2-12\"-->\"x=-10\" .
\n" ); document.write( "So without any other specification in the problem,
\n" ); document.write( "an infinite number of ordered pairs describe point \"U\" ,
\n" ); document.write( "and an infinite number of possible triangles.
\n" ); document.write( "I will draw just the lines \"green%28x=-10%29\" and \"green%28x=14%29\" ,
\n" ); document.write( "and a few of the triangles.
\n" ); document.write( "
\n" ); document.write( "If we want to make triangle \"QTU\" isosceles (don't we all love symmetrical shapes?),
\n" ); document.write( "and we want \"QTU\" named counterclockwise, as square \"QRST\" was,
\n" ); document.write( "then \"U\" is \"U%2814%2C5%29\" .
\n" ); document.write( "
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