document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196022>Question 1196022</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On his way to room, Liza traveled 3 km North and<BR>\n" );
document.write( "4 km West. What is the displacement made by Liza?<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 #828688 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=828688\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Define these points<BR>\n" );
document.write( "A = Liza's starting point<BR>\n" );
document.write( "B = the point 3 km directly north of point A<BR>\n" );
document.write( "C = the point 4 km directly west of point B, which is Liza's ending point\r<BR>\n" );
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document.write( "The points form a right triangle. The 90 degree angle is at point B.<BR>\n" );
document.write( "I recommend drawing out a quick sketch of this. It doesn't need to be perfect or to scale.<BR>\n" );
document.write( "See the diagram at the bottom.\r<BR>\n" );
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document.write( "We can use the pythagorean theorem to find the distance from A (Liza's starting point) to C (Liza's ending point). <BR>\n" );
document.write( "All displacement cares about are these two points. Any stuff in the middle is ignored. <BR>\n" );
document.write( "Think of displacement being the ultimate shortcut you can take when going from the beginning directly to the ending.\r<BR>\n" );
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document.write( "The right triangle has legs of a = 3 and b = 4<BR>\n" );
document.write( "The unknown hypotenuse is c\r<BR>\n" );
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document.write( "Let's apply the pythagorean theorem to solve for c.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+sqrt%28a%5E2%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"c+=+sqrt%28a%5E2%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+sqrt%283%5E2%2B4%5E2%29 ALIGN=MIDDLE  ALT=\"c+=+sqrt%283%5E2%2B4%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+sqrt%289%2B16%29 ALIGN=MIDDLE  ALT=\"c+=+sqrt%289%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+sqrt%2825%29 ALIGN=MIDDLE  ALT=\"c+=+sqrt%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+5 ALIGN=MIDDLE  ALT=\"c+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We have a 3-4-5 right triangle, which is perhaps the most famous of the many pythagorean triples.<BR>\n" );
document.write( "To confirm this is correct, you could use a tool like GeoGebra as shown below<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/tAb5USf.png\">\r<BR>\n" );
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document.write( "Therefore, the distance from A to C is 5 km.<BR>\n" );
document.write( "This is the displacement.\r<BR>\n" );
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document.write( "Answer: <font color=red>5 km</font><BR>\n" );
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