document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=258389>Question 258389</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the shortest distance from (9,5) to 5x + 3y =15 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #190224 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=190224\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Determine the shortest distance from (9,5) to 5x + 3y =15<BR>\n" );
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document.write( "The shortest distance is a perpendicular distance.<BR>\n" );
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document.write( "Find the slope of the given line:<BR>\n" );
document.write( "y = (-5/3)x + 5<BR>\n" );
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document.write( "ANY line perpendicular to that line must <BR>\n" );
document.write( "have a slope = 3/5<BR>\n" );
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document.write( "Find the equation of the line with slope = 3/5 and passing thru (9,5):<BR>\n" );
document.write( "5 = (3/5)9 + b<BR>\n" );
document.write( "5 = (27/5) + b<BR>\n" );
document.write( "b = (25/5)-(27/5)<BR>\n" );
document.write( "b = -2/5<BR>\n" );
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document.write( "Equation you want: y = (3/5)x - (2/5)<BR>\n" );
document.write( "5y = 3x - 2<BR>\n" );
document.write( "3x - 5y = 2<BR>\n" );
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document.write( "Find the point of intersection of the two equations:<BR>\n" );
document.write( "3x-5y = 2<BR>\n" );
document.write( "5x+3y = 15<BR>\n" );
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document.write( "Multiply 1st Eq. by 3; Multiply 2nd equation by 5:<BR>\n" );
document.write( "9x - 15y = 6<BR>\n" );
document.write( "25x- 15y = 75<BR>\n" );
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document.write( "Add and solve for \"x\":<BR>\n" );
document.write( "34x = 81<BR>\n" );
document.write( "x = 81/34<BR>\n" );
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document.write( "Substitute to solve for \"y\":<BR>\n" );
document.write( "3(81/34) - 5y = 6<BR>\n" );
document.write( "243/34 - 5y = 6<BR>\n" );
document.write( "5y = (243-204)/34<BR>\n" );
document.write( "5y = 39/34<BR>\n" );
document.write( "y = (39/170)<BR>\n" );
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document.write( "The point of intersection is (81/34 , 39/170)<BR>\n" );
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document.write( "Find the distance between that point and (9,5)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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