document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62108>Question 62108</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I'm currently doing very poorly in Geometry, but my teacher gave us this problem for extra credit. It's due tomorrow (11/20/06) so if you could get back to me as soon as you can, that'd be fantastic.\r<BR>\n" );
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document.write( "Find the shortest distance from the point (4,0) to the line -2x + 5y = 15.\r<BR>\n" );
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document.write( "Thank you so much!!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #42861 by </B><A HREF=/tutors/aboutme.mpl?userid=rchill><B>rchill(405)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rchill><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=42861\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The shortest distance is going to be a perpendicular line from that point to the given line.  The slope of that perpendicular line is the opposite of the reciprical of the slope of the given line.  Solving for y in order to get the equation of a line in y=mx+b, where m is the slope and b is the y-intercept, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=expr%282%2F5%29x%2B3 ALIGN=MIDDLE  ALT=\"y=expr%282%2F5%29x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which means the slope of the perpendicular line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-expr%285%2F2%29 ALIGN=MIDDLE  ALT=\"-expr%285%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So the equation of the perpendicular line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-expr%285%2F2%29x%2Bb ALIGN=MIDDLE  ALT=\"y=-expr%285%2F2%29x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > and now we need to solve for b.  To do that, substitutue the ordered pair values (4,0) into the equation and get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-expr%285%2F2%294%2Bb ALIGN=MIDDLE  ALT=\"0=-expr%285%2F2%294%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > or b=10.  So the final equation of the perpendicular line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-expr%285%2F2%29x%2B10 ALIGN=MIDDLE  ALT=\"y=-expr%285%2F2%29x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the graph of both lines is below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C200%2C-5%2C5%2C-5%2C5%2C2x%2F5%2B3%2C-5x%2F2%2B10%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C200%2C-5%2C5%2C-5%2C5%2C2x%2F5%2B3%2C-5x%2F2%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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