document.write( "Question 1004861: Find the point on each median that is two-thirds of the distance from the vertec to the midpoint if the vertices of the triangle are A (4,-4), B (10,4) & C (2,6) \n" ); document.write( "
Algebra.Com's Answer #621219 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!
The midpoints are
\n" ); document.write( "(7,0),(6,5),(3,1)\r
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\n" ); document.write( "\n" ); document.write( "The midpoint of the triangle is \"%282%2F3%29s\" the length of the median.
\n" ); document.write( "Find one vertex, and go \"%282%2F3%29s\" the way to the midpoint of the opposite side. Directions matter. Start at the point, and take \"%282%2F3%29s\" the \"x\" value and \"%282%2F3%29s\" the \"y\" value.\r
\n" ); document.write( "\n" ); document.write( "The easiest one is \"%282%2F3%29s\" from (\"2\",\"6\") to (\"7\",\"0\")
\n" ); document.write( "The \"x\"-value is \"%282%2F3%29s\" from \"2\" to \"7\". The distance is \"5\", and \"%282%2F3%29s\" of that is \"%2810%2F3%29\", or \"3.33\".
\n" ); document.write( "So the \"x\"-value is \"5.33\" or \"16%2F3\".
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\n" ); document.write( "The \"y\"-value is \"%282%2F3%29s\" from \"6\" to \"0\", or \"%282%2F3%296=4\". The \"y\"-value is \"2\".\r
\n" ); document.write( "\n" ); document.write( "The midpoint is (\"16%2F3\",\"2\").\r
\n" ); document.write( "\n" ); document.write( "This will work for the other two points to the opposite side midpoint.\r
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\n" ); document.write( "\n" ); document.write( "or, you can do it this way:\r
\n" ); document.write( "\n" ); document.write( "take two vertices and two midpoints and find the equations of the lines passing through one midpoint and opposite vertices\r
\n" ); document.write( "\n" ); document.write( "R(7,0) and C (2,6)\r
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Solved by pluggable solver: Find the equation of line going through points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (7, 0) and (x2, y2) = (2, 6).
\n" ); document.write( " Slope a is \"a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%286-0%29%2F%282-7%29+=+-1.2\".
\n" ); document.write( " Intercept is found from equation \"a%2Ax%5B1%5D%2Bb+=+y%5B1%5D\", or \"-1.2%2A7+%2Bb+=+8.4\". From that,
\n" ); document.write( " intercept b is \"b=y%5B1%5D-a%2Ax%5B1%5D\", or \"b=0--1.2%2A7+=+8.4\".
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\n" ); document.write( " y=(-1.2)x + (8.4)
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\n" ); document.write( " Your graph:
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\n" ); document.write( "\n" ); document.write( "Q(6,5) and A (4,-4)\r
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Solved by pluggable solver: Find the equation of line going through points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (6, 5) and (x2, y2) = (4, -4).
\n" ); document.write( " Slope a is \"a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%28-4-5%29%2F%284-6%29+=+4.5\".
\n" ); document.write( " Intercept is found from equation \"a%2Ax%5B1%5D%2Bb+=+y%5B1%5D\", or \"4.5%2A6+%2Bb+=+-22\". From that,
\n" ); document.write( " intercept b is \"b=y%5B1%5D-a%2Ax%5B1%5D\", or \"b=5-4.5%2A6+=+-22\".
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\n" ); document.write( " y=(4.5)x + (-22)
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\n" ); document.write( " Your graph:
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\n" ); document.write( "\n" ); document.write( "so, your equations are:\r
\n" ); document.write( "\n" ); document.write( "\"y=-1.2x+%2B+8.4\" and
\n" ); document.write( "\"y=4.5x+-22\"
\n" ); document.write( "-----------------find intersection
\n" ); document.write( "since left sides equal, make right sides equal and solve for \"x\"\r
\n" ); document.write( "\n" ); document.write( "\"4.5x+-22=-1.2x+%2B+8.4\"\r
\n" ); document.write( "\n" ); document.write( "\"4.5x+%2B1.2x+=22%2B+8.4\"\r
\n" ); document.write( "\n" ); document.write( "\"5.7x++=30.4\"\r
\n" ); document.write( "\n" ); document.write( "\"x++=30.4%2F5.7\"\r
\n" ); document.write( "\n" ); document.write( "\"x++=304%2F57\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+16%2F3\"\r
\n" ); document.write( "\n" ); document.write( "find \"y\"\r
\n" ); document.write( "\n" ); document.write( "\"y=4.5%2816%2F3%29+-22\"\r
\n" ); document.write( "\n" ); document.write( "\"y=45%2816%2F30%29+-%2822%2A30%29%2F30\"\r
\n" ); document.write( "\n" ); document.write( "\"y=720%2F30+-660%2F30\"\r
\n" ); document.write( "\n" ); document.write( "\"y=60%2F30\"\r
\n" ); document.write( "\n" ); document.write( "\"y=2\"\r
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\n" ); document.write( "\n" ); document.write( "intersection point is at (\"16%2F3\",\"2\") and that is your midpoint\r
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