document.write( "Question 345491: Two vertices of a triangle are (0,6) and (4,0), and the medians intersect at (0,2). Find the third vertex of the triangle. \n" ); document.write( "

Algebra.Com's Answer #247100 by Fombitz(32388) $\"\"$ $\"About$

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A:( $\"0\"$ , $\"6\"$ )
\n" ); document.write( "B:( $\"4\"$ , $\"0\"$ )
\n" ); document.write( "C:( $\"x\"$ , $\"y\"$ )
\n" ); document.write( "Assume that the final vertex is located at( $\"x\"$ , $\"y\"$ ).
\n" ); document.write( "Then the median connecting ( $\"x\"$ , $\"y\"$ ) to the midpoint of $\"AB\"$ , located at ( $\"2\"$ , $\"3\"$ ), has a slope,since it also goes through ( $\"0\"$ , $\"2\"$ ), of,
\n" ); document.write( " $\"m=%283-2%29%2F%282-0%29=1%2F2\"$
\n" ); document.write( "and a y-intercept of $\"2\"$ .
\n" ); document.write( "1. $\"y=%281%2F2%29x%2B2\"$
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\n" ); document.write( "The median connecting ( $\"4\"$ , $\"0\"$ ),( $\"0\"$ , $\"2\"$ ), and the midpoint of $\"AC\"$ has a slope of,
\n" ); document.write( " $\"m=%282-0%29%2F%280-4%29=-1%2F2\"$
\n" ); document.write( "and a y-intercept of $\"2\"$ .
\n" ); document.write( " $\"y=-%281%2F2%29x%2B2\"$
\n" ); document.write( "The midpoint of $\"AC\"$ is ( $\"%28x%2B0%29%2F2\"$ , $\"%28y%2B6%29%2F2\"$ ) or ( $\"x%2F2\"$ , $\"y%2F2%2B3\"$ ).
\n" ); document.write( "It also satisfies the line,
\n" ); document.write( " $\"y=-%281%2F2%29x%2B2\"$
\n" ); document.write( " $\"y%2F2%2B3=-%281%2F2%29%28x%2F2%29%2B2\"$
\n" ); document.write( " $\"2y%2B12=-x%2B8\"$
\n" ); document.write( "2. $\"x%2B2y=-4\"$
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\n" ); document.write( "From eq. 1,
\n" ); document.write( " $\"2y=x%2B4\"$
\n" ); document.write( "Substituting into eq. 2,
\n" ); document.write( " $\"x%2Bx%2B4=-4\"$
\n" ); document.write( " $\"2x=-8\"$
\n" ); document.write( " $\"highlight%28x=-4%29\"$
\n" ); document.write( "Then
\n" ); document.write( " $\"2y=-4%2B4\"$
\n" ); document.write( " $\"2y=0\"$
\n" ); document.write( " $\"highlight%28y=0%29\"$
\n" ); document.write( "The final vertex is located at ( $\"-4\"$ , $\"0\"$ )\r
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