document.write( "Question 926264: Given the points A(-2, 1) and B(4, 5), determine the coordinates of point P on directed line segment that partitions in the ratio 7/3.\r
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\n" ); document.write( "A 7/3 ratio divides the segment into equal parts.
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\n" ); document.write( "The x-coordinate of P is x1 + k • run =
\n" ); document.write( "The y-coordinate of P is y1 + k • rise =
\n" ); document.write( "The coordinates of P are (, ) \n" ); document.write( "

Algebra.Com's Answer #562126 by Edwin McCravy(20056) $\"\"$ $\"About$

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Given the points A(-2, 1) and B(4, 5), determine the coordinates of point P on directed line segment that partitions in the ratio 7/3.
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document.write( "The ratio of the parts is not k.  We calculate k this way:\r\n" );
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document.write( "That is, to find k we must add the numerator to the denominator of the\r\n" );
document.write( "ratio of the two parts.  We plot the point and draw the line connecting them,\r\n" );
document.write( "guessing about where P(?,?) might be:\r\n" );
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document.write( "Now we draw the run (in green) and the rise (in red):\r\n" );
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document.write( "Now we count the blocks and find that the green RUN is 6 units long\r\n" );
document.write( "and that the red RISE is 4 units long.\r\n" );
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document.write( "Now since we know the RUN=6 and the RISE=4, and that \r\n" );
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document.write( "k = 7/10, x1=[x-coordinate of A]=-2, y1=[y-coordinate of A]=1, we are\r\n" );
document.write( "ready to substitute:\r\n" );
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document.write( "The x-coordinate of P is x1 + k • run = -2 + 7/10 • 6 = \r\n" );
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document.write( "      -2 + 42/10 = -2 + 21/5 = -10/5 + 21/5 = 11/5        \r\n" );
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document.write( "The y-coordinate of P is y1 + k • rise = 1 + 7/10 • 4 = \r\n" );
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document.write( "      1 + 28/10 = 1 + 14/5 = 5/5 + 14/5 = 19/5   \r\n" );
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document.write( "The coordinates of P are (11/5,19/5).  Final graph:\r\n" );
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document.write( "Edwin

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