document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203834>Question 203834</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you find the midpoint and the distance of two points which is (1). radical 2 plus (+) 1, radical 2; (2) radical 2 -1 and 2 radical 2? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153802 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=153802\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Short answer: The same way you find any midpoint and the same way you find any distance.<br><BR>\n" );
document.write( "An important idea to understand in Math is that basic logic does not change when the format of the numbers change. Formulas can be used regardless of the types of numbers involved. (The arithmetic may be more difficult for fractions and square roots than it is for \"nice\" whole numbers but the formulas still work.)<BR>\n" );
document.write( "Your points are (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29+%2B+1 ALIGN=MIDDLE  ALT=\"sqrt%282%29+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29+-+1 ALIGN=MIDDLE  ALT=\"sqrt%282%29+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%282%29 ALIGN=MIDDLE  ALT=\"2sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "The midpoint formula: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B1%5D+%2B+x%5B2%5D%29%2F2 ALIGN=MIDDLE  ALT=\"%28x%5B1%5D+%2B+x%5B2%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5B1%5D+%2B+y%5B2%5D%29%2F2 ALIGN=MIDDLE  ALT=\"%28y%5B1%5D+%2B+y%5B2%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Substituting your x and y coordinates we get:<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28sqrt%282%29+%2B+1%29+%2B+%28sqrt%282%29+-+1%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28%28sqrt%282%29+%2B+1%29+%2B+%28sqrt%282%29+-+1%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28sqrt%282%29%29+%2B+%282sqrt%282%29%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28%28sqrt%282%29%29+%2B+%282sqrt%282%29%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Simplifying the numerators we get:<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282sqrt%282%29%29%2F2 ALIGN=MIDDLE  ALT=\"%282sqrt%282%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283sqrt%282%29%29%2F2 ALIGN=MIDDLE  ALT=\"%283sqrt%282%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "The x coordinate fraction will reduce:<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283sqrt%282%29%29%2F2 ALIGN=MIDDLE  ALT=\"%283sqrt%282%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "which is the midpoint.<br><BR>\n" );
document.write( "The distance formula is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%28x%5B2%5D+-x%5B1%5D%29%5E2+%2B+%28y%5B2%5D+-+y%5B1%5D%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%28x%5B2%5D+-x%5B1%5D%29%5E2+%2B+%28y%5B2%5D+-+y%5B1%5D%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting your x and y coordinates into the formula we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%28%28sqrt%282%29+-+1%29+-+%28sqrt%282%29+%2B+1%29%29%5E2+%2B+%28%282sqrt%282%29%29+-+%28sqrt%282%29%29%29%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%28-2%29%5E2+%2B+%28sqrt%282%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%28-2%29%5E2+%2B+%28sqrt%282%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=d+=+sqrt%284+%2B+2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%284+%2B+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=d+=+sqrt%286%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the distance between the two points is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );