document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=92035>Question 92035</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I think this is the correct place to put this. I'm doing a practice packet I have to turn in on the first day of school. Here are the problems.\r<BR>\n" );
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document.write( "Find the distance between the given points.\r<BR>\n" );
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document.write( "1. (-5,-7) and (7, 9)           \r<BR>\n" );
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document.write( "2. (6, -17) and (18, -5)\r<BR>\n" );
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document.write( "If you could tell me the formula and what to do I think I can get it. (Step by step please) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66862 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=66862\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You might recognize this as a Pythagorean theorem problem. If you think about it a little<BR>\n" );
document.write( "you can see that the change in the x distances (horizontal) between the two points is one leg of a <BR>\n" );
document.write( "right triangle, and the change in the y distances (vertical) between the two points is the <BR>\n" );
document.write( "other leg. Then the hypotenuse of the right triangle is the distance between the two points.<BR>\n" );
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document.write( "Plot the two points on a graph. Then extend a vertical line through each point and a horizontal<BR>\n" );
document.write( "line through each point. Where the vertical line intersects with the horizontal line is<BR>\n" );
document.write( "the vertex of a right angle.  Now draw a line that connects the two points.  Notice how<BR>\n" );
document.write( "it is the hypotenuse of a right triangle formed by the horizontal line, the vertical, line<BR>\n" );
document.write( "and the line connecting the two points.  Let's try one of your problems to give you the<BR>\n" );
document.write( "idea. Take the points (-5,-7) and (7,9)<BR>\n" );
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document.write( "Notice that the change in x is from -5 to +7, a distance of 12. Then notice that the change<BR>\n" );
document.write( "in y is from -7 to +9, a distance of 16.<BR>\n" );
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document.write( "Now recall from geometry that the Pythagorean theorem says that the sum of the squares<BR>\n" );
document.write( "of the two legs of a right triangle is equal to the square of the hypotenuse. If one leg is x<BR>\n" );
document.write( "and the other leg is y and the hypotenuse (longest side) is h, then the equation form of the<BR>\n" );
document.write( "Pythagorean theorem can be written as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+=+h%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+=+h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "For this problem we found that x = 12 and y = 16. Substituting these values gives:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%5E2+%2B+16%5E2+=+h%5E2 ALIGN=MIDDLE  ALT=\"12%5E2+%2B+16%5E2+=+h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And squaring each of the numbers on the left side results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144+%2B+256+=+h%5E2 ALIGN=MIDDLE  ALT=\"144+%2B+256+=+h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Adding the two numbers on the left side:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400+=+h%5E2 ALIGN=MIDDLE  ALT=\"400+=+h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and solve for the distance h by taking the square root of both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+20 ALIGN=MIDDLE  ALT=\"h+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this explanation helps you to understand why the distance equation works the way it does.<BR>\n" );
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