document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204346>Question 1204346</A>: <I><SPAN STYLE=\"word-break: break-all;\"> determine the shortest distance from the point e(1,-4) to the line through points of(-5'2) and g(3,4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840542 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The answer from tutor @Mananth is incorrect.  There is an error somewhere in her work.<br><BR>\n" );
document.write( "The method she shows is valid:<BR>\n" );
document.write( "(1) Find the equation of the line through the two given points;<BR>\n" );
document.write( "(2) Find the equation of the line perpendicular to that given line passing through (1,-4);<BR>\n" );
document.write( "(3) Find the point of intersection of the two lines; and<BR>\n" );
document.write( "(4) find the distance between (1,-4) and that point of intersection<br><BR>\n" );
document.write( "Do all those steps correctly and you will get the right answer.<br><BR>\n" );
document.write( "But there is a much faster way to solve the problem.<br><BR>\n" );
document.write( "There is an easy formula for finding the shortest distance from a given point to a given line.<br><BR>\n" );
document.write( "If the equation of the given line is Ax+By+C=0 (the equation must be in that form), and the given point is (p,q), then the shortest distance from the point to the line is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28Ap%2BBq%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29 ALIGN=MIDDLE  ALT=\"%28Ap%2BBq%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "For the given problem, the equation of the line through (-5,2) and (3,4), in the required form, is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4y%2B13=0 ALIGN=MIDDLE  ALT=\"x-4y%2B13=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then, with the given point (1,-4), the shortest distance from the point to the line is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%281%29-4%28-4%29%2B13%29%2Fsqrt%281%5E2%2B4%5E2%29=30%2Fsqrt%2817%29 ALIGN=MIDDLE  ALT=\"%281%281%29-4%28-4%29%2B13%29%2Fsqrt%281%5E2%2B4%5E2%29=30%2Fsqrt%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That gives the shortest distance as 7.276, to 3 decimal places.<br><BR>\n" );
document.write( " </SPAN>\n" );
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