document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=71832>Question 71832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the distance between the points A(4,-3) and B(-4,3).\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51344 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=51344\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation that is used for finding the distance (D) between two points is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+sqrt%28%28x2-x1%29%5E2+%2B%28y2-y1%29%5E2%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28%28x2-x1%29%5E2+%2B%28y2-y1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now let's identify the two points you were given.  Let's call point A (4,-3) point 1 and that<BR>\n" );
document.write( "means that x1 = 4 and y1 = -3. That means that point B (-4, 3) is point 2.  Therefore, <BR>\n" );
document.write( "x2 = -4 and y2 = 3. (If we had let point A be point 2 and point B be point 1, it wouldn't<BR>\n" );
document.write( "make any difference in the answer we get for the distance.  It would still work out the<BR>\n" );
document.write( "same as below even though the values of x1, y1, x2, and y2 would be changed.)<BR>\n" );
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document.write( "Now all we have to do is substitute our values for x1, x2, y1, and y2 into the distance<BR>\n" );
document.write( "equation.  When we do we get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+sqrt%28%28-4-%28%2B4%29%29%5E2+%2B%283-%28-3%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28%28-4-%28%2B4%29%29%5E2+%2B%283-%28-3%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+sqrt%28%28-8%29%5E2+%2B+%28%2B6%29%5E2%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28%28-8%29%5E2+%2B+%28%2B6%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And squaring the terms:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+sqrt%2864+%2B+36%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%2864+%2B+36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which further reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+sqrt%28100%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and taking the square root gives you the answer:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+100 ALIGN=MIDDLE  ALT=\"D+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The most important thing to watch out for in Distance problems like these is to not mix<BR>\n" );
document.write( "up what values are x1, x2, y1, and y2.  Just name one of the points as point 1 and use<BR>\n" );
document.write( "its values as x1 and y1 and name the other point as point 2 and use its values as x2 and<BR>\n" );
document.write( "y2.  Then plug them into the correct places into the Distance equation.<BR>\n" );
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document.write( "Hope this helps you to see how to work the equation and find the distance between <BR>\n" );
document.write( "points.<BR>\n" );
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