document.write( "Question 672501: are these vertices of a square A(-3,1)B(1,4)C(4,0) D(0,-3) JUSTIFY ANSWER AND SHOW WORK THANK YOU \n" ); document.write( "
Algebra.Com's Answer #418073 by mananth(16949)\"\" \"About 
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A(-3,1)B(1,4)C(4,0) D(0,-3)\r
\n" ); document.write( "\n" ); document.write( "Find the slopes of AB,BC,CD,DA\r
\n" ); document.write( "\n" ); document.write( "Slope of AB
\n" ); document.write( "x1 y1 x2 y2
\n" ); document.write( "-3 1 1 4
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\n" ); document.write( "slope m = (y2-y1)/(x2-x1)
\n" ); document.write( "( 4 - 1 )/( 1 - -3 )
\n" ); document.write( "( 3 / 4 )
\n" ); document.write( "m(AB)= 3/4 \r
\n" ); document.write( "\n" ); document.write( "M(BC)
\n" ); document.write( "x1 y1 x2 y2
\n" ); document.write( "4 0 1 4
\n" ); document.write( "
\n" ); document.write( "slope m = (y2-y1)/(x2-x1)
\n" ); document.write( "( 4 - 0 )/( 1 - 4 )
\n" ); document.write( "( 4 / -3 )
\n" ); document.write( "m= -4/3 \r
\n" ); document.write( "\n" ); document.write( "m(CA)
\n" ); document.write( "x1 y1 x2 y2
\n" ); document.write( "4 0 0 -3
\n" ); document.write( "
\n" ); document.write( "slope m = (y2-y1)/(x2-x1)
\n" ); document.write( "( -3 - 0 )/( 0 - 4 )
\n" ); document.write( "( -3 / -4 )
\n" ); document.write( "m= 3/4 \r
\n" ); document.write( "\n" ); document.write( "m(AD)
\n" ); document.write( "x1 y1 x2 y2
\n" ); document.write( "-3 1 0 -3
\n" ); document.write( "
\n" ); document.write( "slope m = (y2-y1)/(x2-x1)
\n" ); document.write( "( -3 - 1 )/( 0 - -3 )
\n" ); document.write( "( -4 / 3 )
\n" ); document.write( "m= -4/3
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\n" ); document.write( "Two lines are having same slopes and two are having slopes negative reciprocal\r
\n" ); document.write( "\n" ); document.write( "So the angles formed are 90 degrees.\r
\n" ); document.write( "\n" ); document.write( "If the distances aer equal then the co ordinates form a square.\r
\n" ); document.write( "\n" ); document.write( "l(AB)
\n" ); document.write( "x1 y1 x2 y2
\n" ); document.write( "
\n" ); document.write( "-3 1 1 4
\n" ); document.write( "d= \"sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29\"
\n" ); document.write( "d= \"sqrt%28%28%09%094%09-%091%09%29%5E2%09%2B%09%28%091%09-%09-3%09%29%5E2%09%29\"
\n" ); document.write( "d= \"sqrt%28%28%09%093%09%29%5E2%09%2B%09%28%094%09%29%5E2%09%29\"
\n" ); document.write( "d= \"sqrt%28%28%09%0925%09%29++%09%29\"
\n" ); document.write( "d= 5 \r
\n" ); document.write( "\n" ); document.write( "l(BC)
\n" ); document.write( "x1 y1 x2 y2
\n" ); document.write( "
\n" ); document.write( "4 0 1 4
\n" ); document.write( "d= \"sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29\"
\n" ); document.write( "d= \"sqrt%28%284-0%29%5E2%09%2B%281-4%29%5E2%29\"
\n" ); document.write( "d= \"sqrt%28%284%29%5E2%09%2B%28-3%29%5E2%09%29\"
\n" ); document.write( "d= \"sqrt%28%28%09%0925%09%29++%09%29\"
\n" ); document.write( "d= 5 \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "l(CD)
\n" ); document.write( "x1 y1 x2 y2
\n" ); document.write( "
\n" ); document.write( "4 0 0 -3
\n" ); document.write( "d= \"sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29\"
\n" ); document.write( "d= \"sqrt%28%28-3-0%29%5E2%2B%280-4%29%5E2%29\"
\n" ); document.write( "d= \"sqrt%28%28-3%29%5E2%09%2B%28-4%29%5E2%09%29\"
\n" ); document.write( "d= \"sqrt%28%28%09%0925%09%29++%09%29\"
\n" ); document.write( "d= 5\r
\n" ); document.write( "\n" ); document.write( "l(DA)\r
\n" ); document.write( "\n" ); document.write( "x1 y1 x2 y2
\n" ); document.write( "
\n" ); document.write( "-3 1 0 -3
\n" ); document.write( "d= \"sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29\"
\n" ); document.write( "d= \"sqrt%28%28%09%09-3%09-%091%09%29%5E2%09%2B%09%28%090%09-%09-3%09%29%5E2%09%29\"
\n" ); document.write( "d= \"sqrt%28%28%09%09-4%09%29%5E2%09%2B%09%28%093%09%29%5E2%09%29\"
\n" ); document.write( "d= \"sqrt%28%28%09%0925%09%29++%09%29\"
\n" ); document.write( "d= 5
\n" ); document.write( "The lengths are all 5 units. and they are at right angles. so it is a square.
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