document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113469>Question 113469</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0536105952/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find the coordinates of the midpoint of the segment with endpoints (-8, -3) and (1, 6). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82589 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=82589\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In order to find the midpoint between the points (-8,-3) and (1,6), 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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So lets find the averages between the two points\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bmid%5D=%28-8%2B1%29%2F2=%28-7%29%2F2=-3.5 ALIGN=MIDDLE  ALT=\"x%5Bmid%5D=%28-8%2B1%29%2F2=%28-7%29%2F2=-3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the x-coordinate of the midpoint is -3.5 (i.e. x=-3.5)\r<BR>\n" );
document.write( "\n" );
document.write( "-----------------------------------------------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bmid%5D=%28-3%2B6%29%2F2=%283%29%2F2=1.5 ALIGN=MIDDLE  ALT=\"y%5Bmid%5D=%28-3%2B6%29%2F2=%283%29%2F2=1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the y-coordinate of the midpoint is 1.5 (i.e. y=1.5)\r<BR>\n" );
document.write( "\n" );
document.write( "-----------------------------------------------------------------------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "Answer:\r<BR>\n" );
document.write( "\n" );
document.write( "Since the coordinates of the midpoint are x=-3.5, y=1.5, this means the midpoint is (-3.5,1.5)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Check:\r<BR>\n" );
document.write( "\n" );
document.write( "Here is a graph to visually see the answer\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C+500%2C+-10%2C+3%2C+-5%2C+8%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+3%2C+-5%2C+8%2C0%29%2C%0D%0Ablue%28line%28-8%2C-3%2C1%2C6%29%29%2C%0D%0Acircle%28-8%2C-3%2C0.05%29%2C%0D%0Acircle%28-8%2C-3%2C0.08%29%2C%0D%0Acircle%281%2C6%2C0.05%29%2C%0D%0Acircle%281%2C6%2C0.08%29%2C%0D%0Acircle%28-3.5%2C1.5%2C0.05%29%2C%0D%0Acircle%28-3.5%2C1.5%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 (-8,-3) and (1,6) with the midpoint (-3.5,1.5)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We could visually verify our answer if we simply draw right triangles from each point like this:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C+500%2C+-10%2C+3%2C+-5%2C+8%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+3%2C+-5%2C+8%2C0%29%2C%0D%0Ablue%28line%28-8%2C-3%2C1%2C6%29%29%2C%0D%0A%0D%0Aline%28-8%2C-3%2C-8%2C%28-3%2B6%29%2F2%29%2C%0D%0Aline%28-8%2C%28-3%2B6%29%2F2%2C-3.5%2C1.5%29%2C%0D%0Aline%28-3.5%2C1.5%2C%28-8%2B1%29%2F2%2C6%29%2C%0D%0Aline%28%28-8%2B1%29%2F2%2C6%2C1%2C6%29%2C%0D%0A%0D%0Acircle%28-8%2C-3%2C0.05%29%2C%0D%0Acircle%28-8%2C-3%2C0.08%29%2C%0D%0Acircle%281%2C6%2C0.05%29%2C%0D%0Acircle%281%2C6%2C0.08%29%2C%0D%0Acircle%28-3.5%2C1.5%2C0.05%29%2C%0D%0Acircle%28-3.5%2C1.5%2C0.08%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here we can see that the two triangles are congruent (they both have a right angle and equal leg lengths), so our answer is verified.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );