document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72569>Question 72569</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 	Suppose you travel north for 35 kilometers then travel east 65 kilometers. How far are you from your starting point?  North and east can be considered the directions of the y- and x-axis respectively. Round to the tenth's place.\r<BR>\n" );
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document.write( "Answer: <BR>\n" );
document.write( "Show work in this space. 	<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 #51906 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=51906\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you scale a piece of graph paper so in the y direction it goes up at least 35 km and in<BR>\n" );
document.write( "the x-direction it goes out at least 65 km, the you can make a sketch of this problem.<BR>\n" );
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document.write( "Put your pencil on the origin and draw a line up 35 km. From this point go to the right 65 km.<BR>\n" );
document.write( "Then draw a line from the origin to the right end of the 65 km line. You should see that <BR>\n" );
document.write( "you have drawn a right triangle with the two legs of 35 km and 65 km and the hypotenuse <BR>\n" );
document.write( "being the line from the origin to the right end of the 65 km line. This hypotenuse is what you<BR>\n" );
document.write( "need to find because it is the distance from the starting point to the end of your trip.<BR>\n" );
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document.write( "Recall the Pythagorean theorem that says in a right triangle the sum of the squares of the<BR>\n" );
document.write( "two legs equals the square of the hypotenuse.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+H%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+H%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can say that a = 35 km, b = 65 km and H is the distance we are trying to find.<BR>\n" );
document.write( "Substitute 35 for a and 65 for b to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2835%29%5E2+%2B+%2865%29%5E2+=+H%5E2 ALIGN=MIDDLE  ALT=\"%2835%29%5E2+%2B+%2865%29%5E2+=+H%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now it's just calculator work.  35 squared is 1225 and 65 squared is 4225. Add these two<BR>\n" );
document.write( "together and you get 5450.  Substitute this into the equation for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5450+=+H%5E2 ALIGN=MIDDLE  ALT=\"5450+=+H%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "Now all you have to do is take the square root of both sides to find that H, the distance you<BR>\n" );
document.write( "have to find, is the square root of 5450.  The answer is 73.82 km which rounds in the <BR>\n" );
document.write( "tenths place to 73.8 km.<BR>\n" );
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document.write( "After the trip north followed by the trip east you are 73.8 miles as the crow flies from<BR>\n" );
document.write( "the starting point.<BR>\n" );
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document.write( "Hope this helps you see the basics of finding distances between points on a graphed problem. </SPAN>\n" );
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