document.write( "Question 960470: Can you help me with this please?
\n" ); document.write( "Find the coordinate, T , this is three-fifths of the distance from A(2,-2) to B(-3,8) \n" ); document.write( "
Algebra.Com's Answer #586998 by rothauserc(4718)\"\" \"About 
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The distance from point A to point B is calculated with the following formula,
\n" ); document.write( "d = sqrt ( (x2-x1)^2 + (y2 - y1)^2 ) = sqrt ( (-3-2)^2 + (8-(-2))^2 ) = sqrt ( 25 + 100) = 5*sqrt(5)
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\n" ); document.write( "now 3/5 * 5*sqrt(5) = 3*sqrt(5) and
\n" ); document.write( "3*sqrt(5) = sqrt (x2 - 2)^2 + (y2 - (-2))^2)
\n" ); document.write( "square both sides of =
\n" ); document.write( "45 = (x-2)^2 + (y+2)^2
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\n" ); document.write( "now we want the equation of the line that connects points A and B
\n" ); document.write( "slope = 8+2 / -5 = -2
\n" ); document.write( "so far we have
\n" ); document.write( "y = -2x +b
\n" ); document.write( "use point A to find b
\n" ); document.write( "-2 = -2*2 +b
\n" ); document.write( "-2 = -4 +b
\n" ); document.write( "b = 2 and
\n" ); document.write( "y = -2x + 2
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\n" ); document.write( "now substitute -2x+2 for y in the above equation (note that it is the equation of a circle with its center at point A)
\n" ); document.write( "45 = (x-2)^2 + (-2x+2+2)^2
\n" ); document.write( "45 = (x-2)^2 + (-2x+4)^2
\n" ); document.write( "45 = x^2-4x+4 + 4x^2-16x+16
\n" ); document.write( "45 = 5x^2-20x+20
\n" ); document.write( "divide both sides of = by 5
\n" ); document.write( "9 = x^2-4x+4
\n" ); document.write( "x^2 -4x -5 = 0
\n" ); document.write( "(x-5)*(x+1) = 0
\n" ); document.write( "we have two intersection points (substitute for x in our line equation)
\n" ); document.write( "(5,-8) and (-1,4)
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\n" ); document.write( "therefore T = (-1,4)\r
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