document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137657>Question 1137657</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact distance from the point D(4,-2) to the line segment joining the points E(1,3) and  F(-4,-2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755515 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=755515\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The distance from D to the line containing E and F is the length of the line segment from D that is perpendicular to the line.<br><BR>\n" );
document.write( "This particular example is easily solved using equations of perpendicular lines.  I'll outline the process; you can fill in the details if you need.<br><BR>\n" );
document.write( "(1) From the coordinates of E and F, we can determine that the equation of the line E and F is y = x+2.<BR>\n" );
document.write( "(2) The slope of the line containing E and F is 1; the slope of a line perpendicular to that line is -1.<BR>\n" );
document.write( "(3) The line with slope -1 passing through D(4,-2) is y = -x+2.<BR>\n" );
document.write( "(4) The intersection of y=x+2 and y=-x+2 is (0,2).<BR>\n" );
document.write( "(5) The distance from (4,-2) to (0,2) is 4*sqrt(2).<br><BR>\n" );
document.write( "ANSWER: The distance from D to the line containing E and F is 4*sqrt(2).<br><BR>\n" );
document.write( "In general, there is a concise formula for finding the distance from a given point to a given line.<br><BR>\n" );
document.write( "If the equation of the line is in the form Ax+By+C=0, and the coordinates of the point are (a,b), then the 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=abs%28%28Aa%2BBb%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29%29 ALIGN=MIDDLE  ALT=\"abs%28%28Aa%2BBb%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In this example, after finding the equation y=x+2 for the line containing E and F, put it in the required form:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y%2B2=0 ALIGN=MIDDLE  ALT=\"x-y%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "and plug the numbers into the formula (A=1, B=-1, C=2; (a,b) = (4,-2):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28%284%2B2%2B2%29%2Fsqrt%281%2B1%29%29+=+8%2Fsqrt%282%29+=+4%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"abs%28%284%2B2%2B2%29%2Fsqrt%281%2B1%29%29+=+8%2Fsqrt%282%29+=+4%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );