document.write( "Question 1193681: the segment joining A(-3, \"-2)\" and B(-1/2 , 3) is extended to a distance equal to 1/5 of its own length. find the new end point closest to point A \n" ); document.write( "

Algebra.Com's Answer #825715 by Boreal(15235) $\"\"$ $\"About$

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The length of the line is sqrt(difference in x s^2+ diff In y^2)=sqrt(6.25+25)=sqrt(31.25), so one-fifth of that added to sqrt(35), and the answer squared equals 45. That is going to be the sum of what is under the radical.\r
\n" ); document.write( "\n" ); document.write( "the equation of the line is y-y1=m(x-x1), m slope, and (x1, y1) a point.
\n" ); document.write( "the slope is -5/-2.5 or 2
\n" ); document.write( "y+2=2(x+3)
\n" ); document.write( "y=2x+4
\n" ); document.write( "graph the line
\n" ); document.write( " $\"graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C2x%2B4%29\"$ \r
\n" ); document.write( "\n" ); document.write( "The line is extended downward (closest to point A)
\n" ); document.write( "the distance is twice as much y as x
\n" ); document.write( "so the sqrt of( (5+2x)^2+(2.5+x)^2)=sqrt 45
\n" ); document.write( "so 25+20x+4x^2+6.25+5x+x^2=45
\n" ); document.write( "5x^2+25x-13.75=0
\n" ); document.write( "x^2+5x-2.75=0 or 4x^2+20x-11=0
\n" ); document.write( "(2x-1)(2x+11)=0
\n" ); document.write( "x=1/2, -5.5
\n" ); document.write( "Use the positive value. The other value would be the answer on the other end
\n" ); document.write( "The new end point is (-3.5, -3) and the new distance is sqrt(45), which is 1.2 * sqrt(31.25) \n" ); document.write( "

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