document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=547180>Question 547180</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to find the equation of the perpendicular erected in the middle of the segment connecting the points (4,-7) and (7,-4)? <BR>\n" );
document.write( "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 #356274 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=356274\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You need 2 things:<BR>\n" );
document.write( "1) slope of the line segment<BR>\n" );
document.write( "2) (x,y) of the midpoint<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "First you find the x-coordinate of the midpoint<BR>\n" );
document.write( "(4,-7) and (7,-4)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+7+%2B+4+%29+%2F+2+=+11%2F2+ ALIGN=MIDDLE  ALT=\"+%28+7+%2B+4+%29+%2F+2+=+11%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now the y-coordinate<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+-4+%2B+%28-7%29+%29+%2F+2++=+-11%2F2+ ALIGN=MIDDLE  ALT=\"+%28+-4+%2B+%28-7%29+%29+%2F+2++=+-11%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The midpoint is at (11/2, -11/2)<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "Now find slope<BR>\n" );
document.write( "slope = change in y / change in x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+=+%28+-4+-%28-7%29+%29+%2F+%28+7+-%28-7%29+%29+ ALIGN=MIDDLE  ALT=\"+m+=+%28+-4+-%28-7%29+%29+%2F+%28+7+-%28-7%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+=+3+%2F+14+%7D%7D%0D%0AAny+line+perpendicular+to+this+line+will+have%0D%0Aa+slope+=+%7B%7B%7B+-%28+1%2Fm+%29+=+-%28+1%2F%283%2F14%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-%281%2Fm%29+=+-14%2F3+ ALIGN=MIDDLE  ALT=\"+-%281%2Fm%29+=+-14%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Now I can use the point-slope formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-14%2F3+=+%28+y+-+%28-11%2F2%29+%29+%2F+%28+x+-+11%2F2+%29+ ALIGN=MIDDLE  ALT=\"+-14%2F3+=+%28+y+-+%28-11%2F2%29+%29+%2F+%28+x+-+11%2F2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-14%2F3+=+%28+y+%2B+11%2F2%29+%2F+%28+x+-+11%2F2+%29+ ALIGN=MIDDLE  ALT=\"+-14%2F3+=+%28+y+%2B+11%2F2%29+%2F+%28+x+-+11%2F2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+%2B+11%2F2+=+%28-14%2F3%29%2A%28+x+-+11%2F2+%29+ ALIGN=MIDDLE  ALT=\"+y+%2B+11%2F2+=+%28-14%2F3%29%2A%28+x+-+11%2F2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+%2B+11%2F2+=+%28-14%2F3%29%2Ax+%2B+154%2F6+ ALIGN=MIDDLE  ALT=\"+y+%2B+11%2F2+=+%28-14%2F3%29%2Ax+%2B+154%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6y+%2B+33+=+-28x+%2B+154+ ALIGN=MIDDLE  ALT=\"+6y+%2B+33+=+-28x+%2B+154+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6y+=+-28x+%2B+121+ ALIGN=MIDDLE  ALT=\"+6y+=+-28x+%2B+121+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-%2814%2F3%29%2Ax+%2B+121%2F6+ ALIGN=MIDDLE  ALT=\"+y+=+-%2814%2F3%29%2Ax+%2B+121%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "Does it go through (11/2, -11/2) ?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-%2814%2F3%29%2Ax+%2B+121%2F6+ ALIGN=MIDDLE  ALT=\"+y+=+-%2814%2F3%29%2Ax+%2B+121%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-11%2F2+=+-%2814%2F3%29%2A%2811%2F2%29+%2B+121%2F6+ ALIGN=MIDDLE  ALT=\"+-11%2F2+=+-%2814%2F3%29%2A%2811%2F2%29+%2B+121%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-33+=+%28-14%29%2A11+%2B+121+ ALIGN=MIDDLE  ALT=\"+-33+=+%28-14%29%2A11+%2B+121+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-33+=+-154+%2B+121+ ALIGN=MIDDLE  ALT=\"+-33+=+-154+%2B+121+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-33+=+-33+ ALIGN=MIDDLE  ALT=\"+-33+=+-33+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "Here's a plot of the lines ( I don't know how to show a line segment,<BR>\n" );
document.write( "so I show it a a continuous line<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-30%2C+30%2C+-30%2C+30%2C+%283%2F14%29%2Ax+-+77%2F14%2C+-%2814%2F3%29%2Ax+%2B+121%2F6+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );