document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1020098>Question 1020098</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the distance between the point (-3,1) and the line y = -x+4. \r<BR>\n" );
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document.write( "I know first I must find the equation of the perpendicular line, and I get y = -x-2. Then, I must find the point of intersection. In order to do this I know I must set both equations equal to one another as shown here: -x+4 = -x-2. This is where I get stuck. Could you please help me?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #636050 by </B><A HREF=/tutors/aboutme.mpl?userid=Cromlix><B>Cromlix(4381)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Cromlix><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=Cromlix><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=636050\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi there,<BR>\n" );
document.write( "If your line => y = -x + 4<BR>\n" );
document.write( "Two lines that are perpendicular<BR>\n" );
document.write( "to one another have gradients (slopes) <BR>\n" );
document.write( "that multiply together to give -1<BR>\n" );
document.write( "m1 x m2 = -1<BR>\n" );
document.write( "If your original line has a gradient<BR>\n" );
document.write( "of -1 the line perpendicular to it<BR>\n" );
document.write( "would have a gradient of 1<BR>\n" );
document.write( "-1 x m2 = -1<BR>\n" );
document.write( "m2 = -1/-1<BR>\n" );
document.write( "m2 = 1<BR>\n" );
document.write( "Using the line equation<BR>\n" );
document.write( "y - b = m(x - a)<BR>\n" );
document.write( "with m = 1<BR>\n" );
document.write( "(a,b) = (-3, 1)<BR>\n" );
document.write( "y - 1 = 1(x - (-3))<BR>\n" );
document.write( "y - 1 = x + 3<BR>\n" );
document.write( "y = x + 3 + 1<BR>\n" );
document.write( "y = x + 4<BR>\n" );
document.write( "Using simultaneous equations:<BR>\n" );
document.write( "y = -x + 4......(1)<BR>\n" );
document.write( "y = x + 4.......(2)<BR>\n" );
document.write( "Rearrange<BR>\n" );
document.write( "y + x = 4........(1)<BR>\n" );
document.write( "y - x = 4........(2)<BR>\n" );
document.write( "Add (1) + (2)<BR>\n" );
document.write( "2y = 8<BR>\n" );
document.write( "y = 4<BR>\n" );
document.write( "Substitute y = 4 into (1)<BR>\n" );
document.write( "y + x = 4<BR>\n" );
document.write( "4 + x = 4<BR>\n" );
document.write( "x = 4 - 4<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "Point of intersection - {0,4)<BR>\n" );
document.write( "Distance between (0,4) and (-3,1)<BR>\n" );
document.write( "&#8730;(x2 - x1)^2 + (y2 - y1)^2<BR>\n" );
document.write( "&#8730;(-3 - 0)^2 + (1 - 4)^2<BR>\n" );
document.write( "&#8730;(9) + (9)<BR>\n" );
document.write( "&#8730;18<BR>\n" );
document.write( "= 4.2 units<BR>\n" );
document.write( "Hope this helps :-) </SPAN>\n" );
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