document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189657>Question 189657</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Distance from a Point to a Line<BR>\n" );
document.write( "6.Find the exact distance from the point D(4,-2) to the line segment joining the points E(1,3) and F(-4,-2).\r<BR>\n" );
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document.write( "pleaseeee help me ...thank you very much!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142313 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=142313\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Distance from a Point to a Line<BR>\n" );
document.write( "6.Find the exact distance from the point D(4,-2) to the line segment joining the points E(1,3) and F(-4,-2). <BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Step 1 - find the slope of the line<BR>\n" );
document.write( "slope, m, = diffy/diffx = (-2-3)/(-4-1)<BR>\n" );
document.write( "m = 1<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Step 2 - find the equation of the line.<BR>\n" );
document.write( "y-y1 = m*(x-x1) where (x1,y1) is either point (E or F)<BR>\n" );
document.write( "y-3 = 1*(x-1)<BR>\n" );
document.write( "y = x+2<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "Step 3 - find the eqn of the line thru the point perpendicular to line EF.  The shortest distance is on the line perpendicular.<BR>\n" );
document.write( "The slope of lines perpendicular is the negative inverse of the slope of the line EF.<BR>\n" );
document.write( "m2 = -1<BR>\n" );
document.write( "use the method from Step 2<BR>\n" );
document.write( "y-y1 = m*(x-x1) (x1,y1) is point D (4,-2)<BR>\n" );
document.write( "y+2 = -1(x-4)<BR>\n" );
document.write( "y = -x + 2<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Step 4, find the point of intersection of the 2 lines<BR>\n" );
document.write( "y = x+2<BR>\n" );
document.write( "y = -x + 2<BR>\n" );
document.write( "------------  Add<BR>\n" );
document.write( "2y = 4<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "--> the point (0,2)<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Last step, find the distance from D to (0,2)<BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28diffy%5E2+%2B+diffx%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28diffy%5E2+%2B+diffx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%5E2+%2B+4%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%284%5E2+%2B+4%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2832%29 ALIGN=MIDDLE  ALT=\"sqrt%2832%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4sqrt%282%29 ALIGN=MIDDLE  ALT=\"4sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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