document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=87944>Question 87944</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the distance between (-3,-2) and (1,4)\r<BR>\n" );
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document.write( "A) square root of 10<BR>\n" );
document.write( "B) 27<BR>\n" );
document.write( "C) 2 square root of 5<BR>\n" );
document.write( "D) 18 square root of 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #63842 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=63842\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Something is wrong here.<BR>\n" );
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document.write( "The distance between the two points is found by using the Pythagorean theorem. The change in<BR>\n" );
document.write( "x values gives you one leg of the triangle, and the change in y values gives you the other<BR>\n" );
document.write( "leg.<BR>\n" );
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document.write( "Let's compute the change in x. In one of the points the x-value is -3. In the other point<BR>\n" );
document.write( "the x-value is +1. So x goes from -3 to +1 and that is a distance of 4 units.<BR>\n" );
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document.write( "Now let's compute the change in y. In one of the points the y-value is -2, and in the other<BR>\n" );
document.write( "point it is +4. So y goes from -2 to +4 and that is a distance of 6 units.<BR>\n" );
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document.write( "So we know that the two legs of the right triangle are 4 and 6. The hypotenuse of the <BR>\n" );
document.write( "triangle is the distance between the points. The Pythagorean theorem tells us that the<BR>\n" );
document.write( "sum of the squares of the two legs is the hypotenuse squared. In equation form this is:<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+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "where a is one of the legs, b is the other leg, and c is the distance we are looking for.<BR>\n" );
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document.write( "Let's call a the x distance of 4 and b the y distance of 6.  Substituting these values we <BR>\n" );
document.write( "get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E2+%2B+6%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"4%5E2+%2B+6%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and squaring out the terms 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=16+%2B+36+=+c%5E2 ALIGN=MIDDLE  ALT=\"16+%2B+36+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Adding the terms on the left side simplifies the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52+=+c%5E2 ALIGN=MIDDLE  ALT=\"52+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now solve for c 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=c+=+sqrt%2852%29+=+sqrt%284%2A13%29+=+sqrt%284%29%2Asqrt%2813%29+=+2%2Asqrt%2813%29 ALIGN=MIDDLE  ALT=\"c+=+sqrt%2852%29+=+sqrt%284%2A13%29+=+sqrt%284%29%2Asqrt%2813%29+=+2%2Asqrt%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you use a calculator to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%2813%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%2813%29+=+7.211102551 ALIGN=MIDDLE  ALT=\"2%2Asqrt%2813%29+=+7.211102551\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So the distance between the two points you were given is 7.211102551 units.<BR>\n" );
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document.write( "But none of your answers matches that value.<BR>\n" );
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document.write( "Answer a) is square root of 10 and in your head you can tell that it has to be a little bigger <BR>\n" );
document.write( "than square root of 9 which is 3 but it is less than the square root of 16 which is 4.  <BR>\n" );
document.write( "Therefore, answer a) is between 3 and 4, which means that it can't match our answer of <BR>\n" );
document.write( "7.211102551.<BR>\n" );
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document.write( "Answer b) is 27. That definitely doesn't match our answer.<BR>\n" );
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document.write( "Answer c) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is less than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%29 ALIGN=MIDDLE  ALT=\"sqrt%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is 3. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be less than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A3 ALIGN=MIDDLE  ALT=\"2%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that means that answer c) is<BR>\n" );
document.write( "less than 6. Therefore, it doesn't match our answer.<BR>\n" );
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document.write( "Finally, Answer d) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"18%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. You know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is greater than 1. If<BR>\n" );
document.write( "it were just 1, then this answer would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2A1+=+18 ALIGN=MIDDLE  ALT=\"18%2A1+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this answer is greater than<BR>\n" );
document.write( "18. Therefore, it can't be our answer of 7.211102551.  <BR>\n" );
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document.write( "None of the answers matches.<BR>\n" );
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document.write( "Like I said at the beginning ... something is wrong here with this problem.<BR>\n" );
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document.write( "Hope this helps you to see your way through the problem.  The answer you are trying to<BR>\n" );
document.write( "match (assuming that the points are correct) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%2813%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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