document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=446070>Question 446070</A>: <I><SPAN STYLE=\"word-break: break-all;\"> QUESTION: Find the midpoint of the segment with the given endpoints. Then find the distance between the points. Write your answer in simplest form. <p>a) (4,2), (6,10) <BR>\n" );
document.write( "<p>b) (-3,5), (4,9)<BR>\n" );
document.write( "			 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #307166 by </B><A HREF=/tutors/aboutme.mpl?userid=Leaf+W.><B>Leaf W.(135)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Leaf+W.><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=Leaf+W.><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=307166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given two points (x1,y1), (x2,y2),<BR>\n" );
document.write( "Midpoint formula: (x,y) of midpoint = (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x1%2Bx2%29%2F2 ALIGN=MIDDLE  ALT=\"%28x1%2Bx2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y1%2By2%29%2F2 ALIGN=MIDDLE  ALT=\"%28y1%2By2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Distance formula: distance = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "***<BR>\n" );
document.write( "1a. (midpoint)<BR>\n" );
document.write( "(x,y) = (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x1%2Bx2%29%2F2 ALIGN=MIDDLE  ALT=\"%28x1%2Bx2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y1%2By2%29%2F2 ALIGN=MIDDLE  ALT=\"%28y1%2By2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "(x,y) = (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2B6%29%2F2 ALIGN=MIDDLE  ALT=\"%284%2B6%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B10%29%2F2 ALIGN=MIDDLE  ALT=\"%282%2B10%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "(x,y) = (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F2 ALIGN=MIDDLE  ALT=\"10%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F2 ALIGN=MIDDLE  ALT=\"12%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "(x,y) = (5, 6)<BR>\n" );
document.write( "Therefore, the midpoint between (4, 2) and (6, 10) is (5, 6).<BR>\n" );
document.write( "***<BR>\n" );
document.write( "1b. (distance)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%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%286-4%29%5E2+%2B+%2810-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%286-4%29%5E2+%2B+%2810-2%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%282%29%5E2+%2B+%288%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%282%29%5E2+%2B+%288%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%284+%2B+64%29 ALIGN=MIDDLE  ALT=\"sqrt%284+%2B+64%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%2868%29 ALIGN=MIDDLE  ALT=\"sqrt%2868%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%2A2%2A17%29 ALIGN=MIDDLE  ALT=\"sqrt%282%2A2%2A17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can pull out one number for every pair within a square root’s factors. Since there are two 2s, you can pull out a two: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28sqrt%2817%29%29 ALIGN=MIDDLE  ALT=\"2%28sqrt%2817%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Therefore, the distance between (4, 2) and (6, 10) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%2817%29 ALIGN=MIDDLE  ALT=\"2sqrt%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "***<BR>\n" );
document.write( "2a. (midpoint)<BR>\n" );
document.write( "(x,y) = (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x1%2Bx2%29%2F2 ALIGN=MIDDLE  ALT=\"%28x1%2Bx2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y1%2By2%29%2F2 ALIGN=MIDDLE  ALT=\"%28y1%2By2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "(x,y) = (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%2B4%29%2F2 ALIGN=MIDDLE  ALT=\"%28-3%2B4%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2B9%29%2F2 ALIGN=MIDDLE  ALT=\"%285%2B9%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "(x,y) = (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2F2 ALIGN=MIDDLE  ALT=\"14%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "(x,y) = (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 7)<BR>\n" );
document.write( "Therefore, the midpoint between (-3, 5) and (4, 9) is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 7).<BR>\n" );
document.write( "***<BR>\n" );
document.write( "2b. (distance)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%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%284-%28-3%29%29%5E2+%2B+%289-5%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%284-%28-3%29%29%5E2+%2B+%289-5%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%284%2B3%29%5E2+%2B+%284%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%284%2B3%29%5E2+%2B+%284%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%287%29%5E2+%2B+16%29 ALIGN=MIDDLE  ALT=\"sqrt%28%287%29%5E2+%2B+16%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%2849+%2B+16%29 ALIGN=MIDDLE  ALT=\"sqrt%2849+%2B+16%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%2865%29 ALIGN=MIDDLE  ALT=\"sqrt%2865%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%2A13%29 ALIGN=MIDDLE  ALT=\"sqrt%285%2A13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are no pairs of numbers so you cannot simplify.<BR>\n" );
document.write( "Therefore, the distance between (-3, 5) and (4, 9) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2865%29 ALIGN=MIDDLE  ALT=\"sqrt%2865%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );