document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196826>Question 1196826</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Verify that the points (2, -1), (5, 5) and (6, -3) is a right triangle. <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 #829838 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=829838\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Define the points as A,B,C<BR>\n" );
document.write( "The order of the labels doesn't matter\r<BR>\n" );
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document.write( "A = (2,-1)<BR>\n" );
document.write( "B = (5,5)<BR>\n" );
document.write( "C = (6,-3)\r<BR>\n" );
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document.write( "Let's find the slope of segment AB<BR>\n" );
document.write( "We'll use the aptly named slope formula (see footnote at the very bottom of the page).<BR>\n" );
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document.write( "The slope of segment AB is 2 = 2/1<BR>\n" );
document.write( "Each time we move up 2 units, we move to the right 1 unit.<BR>\n" );
document.write( "In short: \"Up 2, right 1\".\r<BR>\n" );
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document.write( "Repeat the same idea for the other segments of triangle ABC<BR>\n" );
document.write( "I'll let you do those steps, but here are the slope values so you can check your work:<BR>\n" );
document.write( "slope of BC = -8<BR>\n" );
document.write( "slope of AC = -1/2\r<BR>\n" );
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document.write( "Let's tidy everything up in a summary so far:<BR>\n" );
document.write( "slope of AB = 2<BR>\n" );
document.write( "slope of BC = -8<BR>\n" );
document.write( "slope of AC = -1/2\r<BR>\n" );
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document.write( "Now ask yourself: \"are there any 2 slopes that pair up to multiply to -1?\"<BR>\n" );
document.write( "The answer is \"yes\" because the slopes of AB and AC multiply to 2*(-1/2) = -1\r<BR>\n" );
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document.write( "This is sufficient information to show AB is perpendicular to AC. The two segments meet up at a 90 degree angle (aka right angle). This shows we have a right triangle. The 90 degree angle is located at point A since AB and AC share this letter in common.\r<BR>\n" );
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document.write( "note: if one segment is vertical, then finding the slope is impossible. The slope of a vertical line is undefined. But if you can show one line is vertical and another horizontal, then you'd have a right triangle. All horizontal lines have slope 0.<BR>\n" );
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