document.write( "Question 1074569: Triangle ABC has vertices A(-3,4), B(5,8), and C(6,-3). Find the equation of the medians from vertices A and B. \n" ); document.write( "

Algebra.Com's Answer #689245 by KMST(5328) $\"\"$ $\"About$

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DISCLAIMER: You probably want someone to check your work,
\n" ); document.write( "but I make arithmetic mistakes too, so if our solutions disagree,
\n" ); document.write( "it just may be that yours is right.\r
\n" ); document.write( "\n" ); document.write( "The medians are the lines connecting one vertex to the midpoint of the other side.
\n" ); document.write( "So, we need to connect point $\"A%28-3%2C4%29\"$ to point $\"M\"$ , the midpoint of $\"BC\"$ ,
\n" ); document.write( "and we need to connect point $\"B%285.8%29\"$ to point $\"N\"$ , the midpoint of $\"AC\"$ .
\n" ); document.write( "
\n" ); document.write( "Finding midpoints:
\n" ); document.write( "The coordinates of a midpoint are the averages of the coordinates of the endpoints.
\n" ); document.write( " $\"x%5BM%5D=%285%2B6%29%2F2=11%2F2=5.5\"$ , and
\n" ); document.write( " $\"y%5BM%5D=%288-3%29%2F2=5%2F2=2.5\"$ , giving us $\"M%285.5%2C2.5%29\"$ .
\n" ); document.write( " $\"x%5BN%5D=%28-3%2B6%29%2F2=3%2F2=1.5\"$ , and
\n" ); document.write( " $\"y%5BN%5D=%284-3%29%2F2=1%2F2=0.5\"$ , giving us $\"N%281.5%2C0.5%29\"$ .
\n" ); document.write( "
\n" ); document.write( "Finding the equation for line AM:
\n" ); document.write( "The slope is $\"%282.5-4%29%2F%285.5-%28-3%29%29=-1.5%2F%285.5%2B3%29=-1.5%2F8.5=-3%2F17\"$ .
\n" ); document.write( "The equation for line AM, in $\"highlight%28point-slope%29\"$ form, using point $\"A%28-3%2C4%29\"$ is
\n" ); document.write( " $\"y-4=%28-3%2F17%29%2A%28x-%28-3%29%29\"$ --> $\"highlight%28y-4=-%283%2F17%29%28x%2B3%29%29\"$ .
\n" ); document.write( "If we want the more traditional and unique $\"highlight%28slope-intercept%29\"$ form, we do some more algebra
\n" ); document.write( " $\"y-4=-%283%2F17%29%28x%2B3%29\"$ --> $\"y-4=-%283%2F17%29x-9%2F17\"$ --> $\"y=-%283%2F17%29x-9%2F17%2B4\"$ --> $\"highlight%28y=-%283%2F17%29x%2B59%2F17%29\"$
\n" ); document.write( "
\n" ); document.write( "Finding the equation for line BN:
\n" ); document.write( "The slope is $\"%288-0.5%29%2F%285-1.5%29=7.5%2F3.5=15%2F7\"$ .
\n" ); document.write( "The equation for line BN, in $\"highlight%28point-slope%29\"$ form, using point $\"B%285%2C8%29\"$ is
\n" ); document.write( " $\"highlight%28y-8=%2815%2F7%29%28x-5%29%29\"$ .
\n" ); document.write( "If we want the more traditional and unique $\"highlight%28slope-intercept%29\"$ form, we do some more algebra
\n" ); document.write( " $\"y-8=%2815%2F7%29%28x-5%29\"$ --> $\"y-8=%2815%2F7%29x-75%2F7\"$ --> $\"y=%2815%2F7%29x-75%2F7%2B8\"$ --> $\"highlight%28y=%2815%2F7%29x-19%2F17%29\"$ \n" ); document.write( "

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