document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=978965>Question 978965</A>: <I><SPAN STYLE=\"word-break: break-all;\"> M(0,4) and N(-3, -2)\r<BR>\n" );
document.write( "\n" );
document.write( "a) MN=?<BR>\n" );
document.write( "B) The midpoint of segment NM is (?, ?)<BR>\n" );
document.write( "c) If N is the midpoint of segment MP, then P has coordinates (?, ?)<BR>\n" );
document.write( "d) the slope of live MN is?\r<BR>\n" );
document.write( "\n" );
document.write( "thank you so much for helping me! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #600318 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=600318\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The slope of MN is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+4+-%28-2%29+%29+%2F+%28+0+-%28-3%29+%29+=+%28+4+%2B+2+%29+%2F+3+ ALIGN=MIDDLE  ALT=\"+%28+4+-%28-2%29+%29+%2F+%28+0+-%28-3%29+%29+=+%28+4+%2B+2+%29+%2F+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "slope = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6%2F3+=+2+ ALIGN=MIDDLE  ALT=\"+6%2F3+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "The length of MN is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+%28+0+-%28-3%29+%29%5E2+%2B+%28+4+-%28-2%29+%29%5E2+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+%28+0+-%28-3%29+%29%5E2+%2B+%28+4+-%28-2%29+%29%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+3%5E2+%2B+6%5E2+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+3%5E2+%2B+6%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+9+%2B+36+%29+=+sqrt%28+45+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+9+%2B+36+%29+=+sqrt%28+45+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+45+%29+=+3%2Asqrt%285%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+45+%29+=+3%2Asqrt%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "MN/2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+3%2Asqrt%285%29+%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+%28+3%2Asqrt%285%29+%29+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "x-coordinate of midpoint MN is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+0+%2B%28-3%29+%29+%2F+2+=+-3%2F2+ ALIGN=MIDDLE  ALT=\"+%28+0+%2B%28-3%29+%29+%2F+2+=+-3%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y-coordinate of midpoint MN is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+4+%2B+%28-2%29+%29+%2F+2+=+2%2F2+ ALIGN=MIDDLE  ALT=\"+%28+4+%2B+%28-2%29+%29+%2F+2+=+2%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F2+=+1+ ALIGN=MIDDLE  ALT=\"+2%2F2+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "The midpoint  of MN is at:<BR>\n" );
document.write( "( -3/2, 1 ) <BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "c) If N is the midpoint of segment MP, then P has coordinates (?, ?)<BR>\n" );
document.write( "I know the length of MN is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2Asqrt%285%29+ ALIGN=MIDDLE  ALT=\"+3%2Asqrt%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The length of NP must also = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2Asqrt%285%29+ ALIGN=MIDDLE  ALT=\"+3%2Asqrt%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+MN+%2B+NP+=+MP+ ALIGN=MIDDLE  ALT=\"+MN+%2B+NP+=+MP+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+MP+=+6%2Asqrt%285%29+ ALIGN=MIDDLE  ALT=\"+MP+=+6%2Asqrt%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6%2Asqrt%285%29+=+sqrt%28+%28+0+-+x+%29%5E2+%2B+%28+4+-+y+%29%5E2+%29+ ALIGN=MIDDLE  ALT=\"+6%2Asqrt%285%29+=+sqrt%28+%28+0+-+x+%29%5E2+%2B+%28+4+-+y+%29%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6%2Asqrt%285%29+=+sqrt%28+x%5E2+%2B+16+-+8y+%2B+y%5E2+%29+ ALIGN=MIDDLE  ALT=\"+6%2Asqrt%285%29+=+sqrt%28+x%5E2+%2B+16+-+8y+%2B+y%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Square both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+36%2A5+=+x%5E2+%2B+16+-+8y+%2B+y%5E2+ ALIGN=MIDDLE  ALT=\"+36%2A5+=+x%5E2+%2B+16+-+8y+%2B+y%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B+y%5E2+-+8y+=+180+-+16+ ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+y%5E2+-+8y+=+180+-+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "The slope of MP is the same as MN, which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+ ALIGN=MIDDLE  ALT=\"+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+=+%28+y+-+4+%29+%2F+%28+x+-+0+%29+ ALIGN=MIDDLE  ALT=\"+2+=+%28+y+-+4+%29+%2F+%28+x+-+0+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+=+y+-+4+ ALIGN=MIDDLE  ALT=\"+2x+=+y+-+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2x+%2B+4+ ALIGN=MIDDLE  ALT=\"+y+=+2x+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By substitutioon:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B+%28+2x+%2B+4+%29%5E2+-8%2A%28+2x+%2B+4+%29+=+164+ ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+%28+2x+%2B+4+%29%5E2+-8%2A%28+2x+%2B+4+%29+=+164+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B+4x%5E2+%2B+16x+%2B+16+-+16x+-+32+=+164+ ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+4x%5E2+%2B+16x+%2B+16+-+16x+-+32+=+164+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x%5E2+=+164+-+16+%2B+32+ ALIGN=MIDDLE  ALT=\"+5x%5E2+=+164+-+16+%2B+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x%5E2+=+180+ ALIGN=MIDDLE  ALT=\"+5x%5E2+=+180+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+=+36+ ALIGN=MIDDLE  ALT=\"+x%5E2+=+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+6+ ALIGN=MIDDLE  ALT=\"+x+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2x+%2B+4+ ALIGN=MIDDLE  ALT=\"+y+=+2x+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2%2A6+%2B+4+ ALIGN=MIDDLE  ALT=\"+y+=+2%2A6+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+16+ ALIGN=MIDDLE  ALT=\"+y+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So,  point P has coordinates ( 6,16 )<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "Does the slope of MP = 2?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+16+-+4+%29+%2F+%28+6+-+0+%29+=+2+ ALIGN=MIDDLE  ALT=\"+%28+16+-+4+%29+%2F+%28+6+-+0+%29+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12%2F6+=+2+ ALIGN=MIDDLE  ALT=\"+12%2F6+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+=+2+ ALIGN=MIDDLE  ALT=\"+2+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "Hope all this helps<BR>\n" );
document.write( "Here's a plot of the line going through M, N, and P<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+20%2C+2x+%2B+4+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+20%2C+2x+%2B+4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );