document.write( "Question 867354: Please help me solve this word problem An equilateral triangle is plotted on a coordinate plane with two vertices at (0,0) and (10,0). What would the coordinates be before the third vertex? \n" ); document.write( "

Algebra.Com's Answer #522965 by mananth(16946) $\"\"$ $\"About$

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let the third vertex be A
\n" ); document.write( "A(x,y), B(0,0) C(10,0)\r
\n" ); document.write( "\n" ); document.write( "distance AB=BC=CA =10( equlateral triangle)\r
\n" ); document.write( "\n" ); document.write( "distance formula
\n" ); document.write( " $\"d=+sqrt+%28%28x1-x2%29%5E2%2B%28y1-y2%29%5E2%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"d%5E2=%28%28x1-x2%29%5E2%2B%28y1-y2%29%5E2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "AB = x^2-y^2
\n" ); document.write( "AC=(x-10)^2+y2
\n" ); document.write( "AB=AC\r
\n" ); document.write( "\n" ); document.write( "x^2-y^2=(x-10)^2+y2
\n" ); document.write( "x^2+y^2=(x^2-20x+100+y2)\r
\n" ); document.write( "\n" ); document.write( "20x=100
\n" ); document.write( "x=5
\n" ); document.write( "Plug x
\n" ); document.write( "x^2+y^2=100
\n" ); document.write( "25+y^2=100\r
\n" ); document.write( "\n" ); document.write( "y^2=75
\n" ); document.write( "y=+/-5sqrt(3)\r
\n" ); document.write( "\n" ); document.write( "A (x,5sqrt(3)) , (5,-5sqrt(3))
\n" ); document.write( " \n" ); document.write( "

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