document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=924137>Question 924137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the coordinates of Q given the M is the midpoint of PQ.  P(6,-2),M(0,5),Q(?,?) Thanks for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #560650 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=560650\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(6,-2),M(0,5),Q(x2,y2)\r<BR>\n" );
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document.write( "Since formula for midpoint is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x1+%2B+x2%29+%2F+2 ALIGN=MIDDLE  ALT=\"%28x1+%2B+x2%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y1+%2B+y2%29+%2F+2 ALIGN=MIDDLE  ALT=\"%28y1+%2B+y2%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then formula for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x2 ALIGN=MIDDLE  ALT=\"x2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y2 ALIGN=MIDDLE  ALT=\"y2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x2+=+2%28Mx%29+-+x1 ALIGN=MIDDLE  ALT=\"x2+=+2%28Mx%29+-+x1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y2+=+2%28My%29+-+y1 ALIGN=MIDDLE  ALT=\"y2+=+2%28My%29+-+y1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Mx ALIGN=MIDDLE  ALT=\"Mx\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > coordinate of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=midpoint ALIGN=MIDDLE  ALT=\"midpoint\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=My ALIGN=MIDDLE  ALT=\"My\"   DISABLED_style= \"max-width:90%; height:auto;\" > the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > coordinate of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=midpoint ALIGN=MIDDLE  ALT=\"midpoint\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x2+=+2%28Mx%29+-+x1 ALIGN=MIDDLE  ALT=\"x2+=+2%28Mx%29+-+x1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x2+=+2%280%29+-+6 ALIGN=MIDDLE  ALT=\"x2+=+2%280%29+-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x2+=+0+-+6 ALIGN=MIDDLE  ALT=\"x2+=+0+-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x2+=+-6 ALIGN=MIDDLE  ALT=\"x2+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y2+=+2%28My%29+-+y1 ALIGN=MIDDLE  ALT=\"y2+=+2%28My%29+-+y1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y2+=+2%285%29+-+%28-2%29 ALIGN=MIDDLE  ALT=\"y2+=+2%285%29+-+%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y2+=+10+%2B2 ALIGN=MIDDLE  ALT=\"y2+=+10+%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y2+=12 ALIGN=MIDDLE  ALT=\"y2+=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, Q(x2,y2)=Q(-6,12)\r<BR>\n" );
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document.write( "Checking:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M+=+%28x1+%2B+x2%29+%2F+2 ALIGN=MIDDLE  ALT=\"M+=+%28x1+%2B+x2%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y1+%2B+y2%29+%2F+2 ALIGN=MIDDLE  ALT=\"%28y1+%2B+y2%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M+=+%286+%2B%28-6%29%29+%2F+2 ALIGN=MIDDLE  ALT=\"M+=+%286+%2B%28-6%29%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2+%2B+12%29+%2F+2 ALIGN=MIDDLE  ALT=\"%28-2+%2B+12%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M+=+%286-6%29+%2F+2 ALIGN=MIDDLE  ALT=\"M+=+%286-6%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2+%2B+12%29+%2F+2 ALIGN=MIDDLE  ALT=\"%28-2+%2B+12%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M+=+0%2F+2 ALIGN=MIDDLE  ALT=\"M+=+0%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+%2F+2 ALIGN=MIDDLE  ALT=\"10+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M ALIGN=MIDDLE  ALT=\"M\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We got the right midpoint.\r<BR>\n" );
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document.write( "Thus, the coordinates of Q are (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12 ALIGN=MIDDLE  ALT=\"+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );