document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175137>Question 175137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with the following question<BR>\n" );
document.write( "Do points P(-2,-2),Q(4,1) and R(2,4) form a right triangle? justify your answer. How can you find the answer by calculation alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130281 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=130281\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> in order for this to be a right triangle, one of the sides must be perpendicular to one of the other sides.<BR>\n" );
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document.write( "in order for that to happen, the slope of one of the sides must be a negative reciprocal of the slope of one of the other sides.<BR>\n" );
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document.write( "slope = (y2-y1)/(x2-x1)<BR>\n" );
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document.write( "slope 1 = (1-(-2)/(4-(-2) = 3/6 = 1/2<BR>\n" );
document.write( "slope 2 = (4-1)/(2-4) = 3/-2 = -3/2<BR>\n" );
document.write( "slope 3 = (4-(-2)/(2-(-2) = 6/4 = 3/2<BR>\n" );
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document.write( "a negative reciprocal of 1/2 is -2.<BR>\n" );
document.write( "a negative reciprocal of -3/2 = 2/3<BR>\n" );
document.write( "a negative reciprocal of 3/2 = -2/3<BR>\n" );
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document.write( "none of slopes of these sides match the perpendicular criteria.<BR>\n" );
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document.write( "also, if this was a right triangle, then a^2 + b^2 = c^2, with c being the longest side.<BR>\n" );
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document.write( "the lengths of each of the sides squared are:<BR>\n" );
document.write( "side 1:  3^2 + 6^2 = 9 + 36 = 45<BR>\n" );
document.write( "side 2:  6^2 + 4^2 = 36 + 16 = 52<BR>\n" );
document.write( "side 3:  3^2 + (-2)^2 = 9 + 4 = 13<BR>\n" );
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document.write( "45 + 13 = 58 not equal to 52.<BR>\n" );
document.write( "this is not a right triangle.<BR>\n" );
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document.write( "i vote no.\r<BR>\n" );
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