document.write( "Question 1041673: Given a triangle whose vertices are A(4,-4) B(10,-4) and C(2,6). Find the point on each median that is two-thirds of the distance from the vertex to the midpoint of the opposite side. \n" ); document.write( "

Algebra.Com's Answer #656661 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "\r\n" );
document.write( "A median of a triangle IS the line from the vertex to the \r\n" );
document.write( "midpoint of the opposite side. \r\n" );
document.write( "\r\n" );
document.write( "The 3 medians of every triangle intersect in a point that IS \r\n" );
document.write( "two-thirds of the distance from the vertex to the midpoint \r\n" );
document.write( "of the opposite side.\r\n" );
document.write( "\r\n" );
document.write( "Therefore you do not have to be concerned at all with the \r\n" );
document.write( "\"two-thirds\" part.  Where they intersect will automatically \r\n" );
document.write( "take care of that fact.  Here's what you do:\r\n" );
document.write( "\r\n" );
document.write( "1.  Use the midpoint point formula to find the midpoint of\r\n" );
document.write( "any two of the three sides. [All three medians are drawn \r\n" );
document.write( "above in green, but you need only pick two of them]\r\n" );
document.write( "\r\n" );
document.write( "2.  Find the equations of those two medians using\r\n" );
document.write( "\r\n" );
document.write( "A. The slope formula.\r\n" );
document.write( "B. The point slope formula.\r\n" );
document.write( "\r\n" );
document.write( "3. Solve the system of the two equations of medians by either\r\n" );
document.write( "\r\n" );
document.write( "A. Substitution, or\r\n" );
document.write( "B. Elimination. \r\n" );
document.write( "\r\n" );
document.write( "4.  The x and y values you get for 3 will be the coordinates\r\n" );
document.write( "of the desired point.\r\n" );
document.write( "\r\n" );
document.write( "If you have any trouble, tell me in the thank-you note form \r\n" );
document.write( "below and I'll get back to you by email.  No charge ever!\r\n" );
document.write( "I do this only as a hobby.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );