document.write( "Question 716743: Given the coordinates
\n" ); document.write( "M(-8,-1)
\n" ); document.write( "A(-2,5)
\n" ); document.write( "T(3,7)
\n" ); document.write( "H(-3,1)
\n" ); document.write( "- Plot the quadrilateral on the plane.
\n" ); document.write( "- Prove that the quadrilateral is a parallelogram. Use mathmatics to justify your answer.
\n" ); document.write( "- What special parallelogram is quadrilateral MATH? \n" ); document.write( "
Algebra.Com's Answer #439964 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Given the coordinates
\n" ); document.write( "M(-8,-1)
\n" ); document.write( "A(-2,5)
\n" ); document.write( "T(3,7)
\n" ); document.write( "H(-3,1)
\n" ); document.write( "- Plot the quadrilateral on the plane.
\n" ); document.write( "-
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "

\n" ); document.write( "Prove that the quadrilateral is a parallelogram. Use mathmatics to justify your answer.
\n" ); document.write( "
\r\n" );
document.write( "Use the slope formula\r\n" );
document.write( "\r\n" );
document.write( "m = \"%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"\r\n" );
document.write( "\r\n" );
document.write( "to show that MA ∥ HT\r\n" );
document.write( "\r\n" );
document.write( "To find the slope of MA\r\n" );
document.write( "\r\n" );
document.write( "Use (x1,y1) = (-8,-1)\r\n" );
document.write( "and where (x2,y2) = (-2,5)\r\n" );
document.write( "\r\n" );
document.write( "m = \"%28%285%29-%28-1%29%29%2F%28%28-2%29-%28-8%29%29\" = \"%285%2B1%29%2F%28-2%2B8%29\" = \"6%2F6\" = 1\r\n" );
document.write( "\r\n" );
document.write( "To find the slope of HT\r\n" );
document.write( "\r\n" );
document.write( "Use (x1,y1) = (-3,1)\r\n" );
document.write( "and where (x2,y2) = (3,7)\r\n" );
document.write( "\r\n" );
document.write( "m = \"%28%287%29-%281%29%29%2F%28%283%29-%28-3%29%29\" = \"%287-1%29%2F%283%2B3%29\" = \"6%2F6\" = 1\r\n" );
document.write( "\r\n" );
document.write( "So MA ∥ HT because the have the same slope of 1 each.\r\n" );
document.write( "\r\n" );
document.write( "--------------\r\n" );
document.write( "\r\n" );
document.write( "Use the slope formula\r\n" );
document.write( "\r\n" );
document.write( "m = \"%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"\r\n" );
document.write( "\r\n" );
document.write( "to show that MH ∥ AT\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To find the slope of MH\r\n" );
document.write( "\r\n" );
document.write( "Use (x1,y1) = (-8,-1)\r\n" );
document.write( "and where (x2,y2) = (-3,1)\r\n" );
document.write( "\r\n" );
document.write( "m = \"%28%281%29-%28-1%29%29%2F%28%28-3%29-%28-8%29%29\" = \"%281%2B1%29%2F%28-3%2B8%29\" = \"2%2F5\" \r\n" );
document.write( "\r\n" );
document.write( "To find the slope of AT\r\n" );
document.write( "\r\n" );
document.write( "Use (x1,y1) = (-2,5)\r\n" );
document.write( "and where (x2,y2) = (3,7)\r\n" );
document.write( "\r\n" );
document.write( "m = \"%28%287%29-%285%29%29%2F%28%283%29-%28-2%29%29\" = \"%287-5%29%2F%283%2B2%29\" = \"2%2F5\"\r\n" );
document.write( "\r\n" );
document.write( "So MH ∥ AT because the have the same slope of \"2%2F5\" each.\r\n" );
document.write( "\r\n" );
document.write( "----------------------------------------------------- \r\n" );
document.write( "

\n" ); document.write( "- What special parallelogram is quadrilateral MATH?
\n" ); document.write( "
\r\n" );
document.write( "This parallelogram is neither a rhombus nor a rectangle, so\r\n" );
document.write( "there is nothing special about this parallelogram other\r\n" );
document.write( "than the fact that its coordinates spell \"MATH\", and math\r\n" );
document.write( "happens to be the name of the subject you are studying.  :)\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );