document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72641>Question 72641</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the line that is perpendicular to the line <BR>\n" );
document.write( "segment from (-3, 4) to (1, -2) and passes through the line segment <BR>\n" );
document.write( "at its midpoint.\r<BR>\n" );
document.write( "\n" );
document.write( "I'm not sure how to do the line when it is perpendicular, please help!<BR>\n" );
document.write( "ThAnKs! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51939 by </B><A HREF=/tutors/aboutme.mpl?userid=checkley75><B>checkley75(3666)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=checkley75><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=51939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The slope is the key here.<BR>\n" );
document.write( "Thus slope =(y2-y1)/(x2-x1)<BR>\n" );
document.write( "(-2-4)/(1+3)<BR>\n" );
document.write( "-6/4<BR>\n" );
document.write( "-3/2 this is the slope through the 2 points.<BR>\n" );
document.write( "the line equation here is:<BR>\n" );
document.write( "4=-3/2*-3+b<BR>\n" );
document.write( "4=9/2+b<BR>\n" );
document.write( "b=4-9/2<BR>\n" );
document.write( "b=4-4.5<BR>\n" );
document.write( "b=-.5<BR>\n" );
document.write( "thus the equation for this line is y=-3x/2-.5<BR>\n" );
document.write( "the perpendicular line has a slope that is the negative reciprical of this slope. Thus:<BR>\n" );
document.write( "this slope =2/3. the mid point of the line through (-3,4)(1,-2) is:<BR>\n" );
document.write( "mid point of x=(1+3)2=4/2=2 or -3+2=-1 or 1-2=-1 so the x value is x=-1<BR>\n" );
document.write( "mid point of y=(2+4)/2=6/2=3 or 4-3=1 or -2+3=1 so the midpoint is y=1<BR>\n" );
document.write( "now we have a point & the slope thus the line equation is:<BR>\n" );
document.write( "Y=mX+b<BR>\n" );
document.write( "1=2/3*-1+b<BR>\n" );
document.write( "1=-2/3+b<BR>\n" );
document.write( "b=1-2/3<BR>\n" );
document.write( "b=1/3 therefore the equation is:<BR>\n" );
document.write( "y=2/3x+1/3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+y+=+2x%2F3+%2B1%2F3%2C+y+=+-3x%2F2+-.5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+y+=+2x%2F3+%2B1%2F3%2C+y+=+-3x%2F2+-.5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (graph 300x300 pixels, x from -10 to 10, y from -10 to 10, of TWO functions y = 2x/3 +1/3 and y = -3x/2 -.5 ).  <BR>\n" );
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