document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=89400>Question 89400</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the midpoint of the line segment with endpoints (5,-2) and (-3,12). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64985 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=64985\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In order to find the midpoint, we need to average each corresponding coordinate. In other words, we need to add up the corresponding coordinates and divide the sum by 2.\r<BR>\n" );
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document.write( "So lets find the averages between the two points\r<BR>\n" );
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document.write( "To find <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large  \textrm{x_{mid}}\">, average the x-coordinates between the two points\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bmid%5D=%285%2B-3%29%2F2=%282%29%2F2=1 ALIGN=MIDDLE  ALT=\"x%5Bmid%5D=%285%2B-3%29%2F2=%282%29%2F2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the x-coordinate of the midpoint is 1 (i.e. x=1)\r<BR>\n" );
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document.write( "To find <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large  \textrm{y_{mid}}\">, average the y-coordinates between the two points\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bmid%5D=%28-2%2B12%29%2F2=%2810%29%2F2=5 ALIGN=MIDDLE  ALT=\"y%5Bmid%5D=%28-2%2B12%29%2F2=%2810%29%2F2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the y-coordinate of the midpoint is 5 (i.e. y=5)\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "Since the coordinates of the midpoint are x=1, y=5, this means the midpoint is (1,5)\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "Here is a graph to visually see the answer\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C+500%2C+-5%2C+7%2C+-4%2C+14%2C%0D%0Agraph%28500%2C+500%2C+-5%2C+7%2C+-4%2C+14%2C0%29%2C%0D%0Ablue%28line%285%2C-2%2C-3%2C12%29%29%2C%0D%0Acircle%285%2C-2%2C0.05%29%2C%0D%0Acircle%285%2C-2%2C0.08%29%2C%0D%0Acircle%28-3%2C12%2C0.05%29%2C%0D%0Acircle%28-3%2C12%2C0.08%29%2C%0D%0Acircle%281%2C5%2C0.05%29%2C%0D%0Acircle%281%2C5%2C0.08%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of the line segment with the endpoints (5,-2) and (-3,12) with the midpoint (1,5)\r<BR>\n" );
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document.write( "We could visually verify our answer if we simply draw right triangles from each point like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C+500%2C+-5%2C+7%2C+-4%2C+14%2C%0D%0Agraph%28500%2C+500%2C+-5%2C+7%2C+-4%2C+14%2C0%29%2C%0D%0Ablue%28line%285%2C-2%2C-3%2C12%29%29%2C%0D%0A%0D%0Aline%285%2C-2%2C5%2C%28-2%2B12%29%2F2%29%2C%0D%0Aline%285%2C%28-2%2B12%29%2F2%2C1%2C5%29%2C%0D%0Aline%281%2C5%2C%285%2B-3%29%2F2%2C12%29%2C%0D%0Aline%28%285%2B-3%29%2F2%2C12%2C-3%2C12%29%2C%0D%0A%0D%0Acircle%285%2C-2%2C0.05%29%2C%0D%0Acircle%285%2C-2%2C0.08%29%2C%0D%0Acircle%28-3%2C12%2C0.05%29%2C%0D%0Acircle%28-3%2C12%2C0.08%29%2C%0D%0Acircle%281%2C5%2C0.05%29%2C%0D%0Acircle%281%2C5%2C0.08%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here we can see that the two triangles are congruent, so our answer is verified.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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