document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84792>Question 84792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I don't know if this is the correct section for this.  Find the distance between (-4,0) and (-5,-3). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61084 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=61084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a Pythagorean theorem problem.  <BR>\n" );
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document.write( "Notice that the distance between the x values of the two points that are given is a magnitude <BR>\n" );
document.write( "of 1 which you can get by this subtraction:  [-4 - (-5) = -4 + 5 = +1]. <BR>\n" );
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document.write( "The change in the y values will be at right angles to the change in the x values which<BR>\n" );
document.write( "we found to be 1. The magnitude of the change in the y values is 3 which you can get by<BR>\n" );
document.write( "the subtraction [0 - (-3) = 0 + 3 = 3].<BR>\n" );
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document.write( "In summary the change in x is 1 and the change in y is 3.  These are the legs of a right triangle<BR>\n" );
document.write( "whose hypotenuse is the straight line distance between the points.  Call this hypotenuse D<BR>\n" );
document.write( "and you can then write the Pythagorean equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5E2+%2B+3%5E2+=+D%5E2 ALIGN=MIDDLE  ALT=\"1%5E2+%2B+3%5E2+=+D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The terms on the left side of this equation square out and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2B+9+=+D%5E2 ALIGN=MIDDLE  ALT=\"1+%2B+9+=+D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add the two terms on the left side and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+=+D%5E2 ALIGN=MIDDLE  ALT=\"10+=+D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To find D just take the square root of both sides:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+sqrt%2810%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And that's the answer you were looking for.<BR>\n" );
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document.write( "It might help you to see what's going on in this method if you plot the two points and<BR>\n" );
document.write( "then trace the horizontal path from the first point until you are directly over the second <BR>\n" );
document.write( "point. At this this point trace the path vertically down to the second point. Then draw<BR>\n" );
document.write( "a line connecting the two points. You should recognize the right triangle and be able to<BR>\n" );
document.write( "see that the lengths of the two legs are 1 and 3 units long.  The rest is just application<BR>\n" );
document.write( "of the Pythagorean theorem which says that if you square the two legs and add these squares,<BR>\n" );
document.write( "the result will equal the square of the hypotenuse which in this case is the direct line<BR>\n" );
document.write( "distance between the two points.  [Harder to explain this than it actually is. Once you <BR>\n" );
document.write( "see what's going on, it becomes easier to work distance problems of this type.]<BR>\n" );
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document.write( "Hope this helps you to see your way through distance problems when you are given two points.<BR>\n" );
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