document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=647495>Question 647495</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the distance between the following points.<BR>\n" );
document.write( "(8,5) and (0,20) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #406238 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=406238\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula for distance is simply (maybe not simply) \r<BR>\n" );
document.write( "\n" );
document.write( "Where (x1,y1) and (x2,y2) are just two points.\r<BR>\n" );
document.write( "\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;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "------<BR>\n" );
document.write( "If you understand the distance formula you can skip this.\r<BR>\n" );
document.write( "\n" );
document.write( "This formula is NOT random.\r<BR>\n" );
document.write( "\n" );
document.write( "This formula pieces together slope and the Pythagorean Theorem.\r<BR>\n" );
document.write( "\n" );
document.write( "Recall that for slope  m = (change in y)/(change in x) = (y2-y1)/(x2-x1).\r<BR>\n" );
document.write( "\n" );
document.write( "Now, visualize the distance from y1 to y2 and x1 to x2 as sides of a right triangle. x1 to x2 would be side a and y1 to y2 would be side b. The distance would be our hypotenuse, c. Let d be distance. So (c=d).\r<BR>\n" );
document.write( "\n" );
document.write( "a^2 + b^2 = c^2\r<BR>\n" );
document.write( "\n" );
document.write( "(x2-x1)^2 + (y2-y1)^2 = c^2\r<BR>\n" );
document.write( "\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+=+c ALIGN=MIDDLE  ALT=\"sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29+=+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\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+=+d ALIGN=MIDDLE  ALT=\"sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29+=+d\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Now onto your problem.<BR>\n" );
document.write( "------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "(8,5) and (0,20) are our points.\r<BR>\n" );
document.write( "\n" );
document.write( "x1 = 8<BR>\n" );
document.write( "y1 = 5<BR>\n" );
document.write( "x2 = 0<BR>\n" );
document.write( "y2 = 20\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%280-8%29%5E2+%2B+%2820-5%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%280-8%29%5E2+%2B+%2820-5%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%28-8%29%5E2+%2B+15%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28-8%29%5E2+%2B+15%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%2864+%2B+225%29 ALIGN=MIDDLE  ALT=\"sqrt%2864+%2B+225%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%28289%29 ALIGN=MIDDLE  ALT=\"sqrt%28289%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+=+17 ALIGN=MIDDLE  ALT=\"d+=+17\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );