document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207839>Question 1207839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The coordinates of points A, B, and C are A(-4, 6), B(-1, 2), and C(2,-2). \r<BR>\n" );
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document.write( "(a) Show that AB = BC by using the distance formula. \r<BR>\n" );
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document.write( "(b) Show that AB + BC = AC by using the distance formula. \r<BR>\n" );
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document.write( "(c) What can you conclude from parts (a) and (b)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845968 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=845968\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Let's find the distance from A to B.<BR>\n" );
document.write( "A = (x1,y1) = (-4,6)<BR>\n" );
document.write( "B = (x2,y2) = (-1,2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28+%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2+%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28+%28x1-x2%29%5E2+%2B+%28y1-y2%29%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=d+=+sqrt%28+%28-3%29%5E2+%2B+%284%29%5E2+%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28+%28-3%29%5E2+%2B+%284%29%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=d+=+sqrt%28+9+%2B+16+%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28+9+%2B+16+%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=d+=+5 ALIGN=MIDDLE  ALT=\"d+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The distance from A to B is exactly 5 units.<BR>\n" );
document.write( "Therefore, segment AB is 5 units long.\r<BR>\n" );
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document.write( "Follow similar steps to compute the length of BC.<BR>\n" );
document.write( "I'll let the student do this part.<BR>\n" );
document.write( "You should get BC = 5 as the result. <BR>\n" );
document.write( "This will prove AB = BC.\r<BR>\n" );
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document.write( "I'll also leave the scratch work for computing the length of AC to the student.<BR>\n" );
document.write( "You should get AC = 10\r<BR>\n" );
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document.write( "This confirms that AB+BC = AC is the case since 5+5 = 10.<BR>\n" );
document.write( "Since AB = BC, we have proven that B is the midpoint of AC.\r<BR>\n" );
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document.write( "Side note: The equation 4x+3y = 2 goes through points A,B, and C.<BR>\n" );
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