document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208013>Question 1208013</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that the points A = (-2,0), B = (-4,4), and C = (8,5) are the vertices of a right triangle in two ways: \r<BR>\n" );
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document.write( "(a)By using the converse of the Pythagorean Theorem \r<BR>\n" );
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document.write( "(b)By using the slopes of the lines joining the vertices </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846128 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=846128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The other tutor has discussed part (a).<BR>\n" );
document.write( "I'll focus on part (b) only.\r<BR>\n" );
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document.write( "Use the slope formula to find the slope of line AB.<BR>\n" );
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document.write( "Line AB has slope -2.\r<BR>\n" );
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document.write( "Follow a similar process to find:<BR>\n" );
document.write( "line BC has slope 1/12<BR>\n" );
document.write( "line AC has slope 1/2\r<BR>\n" );
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document.write( "Compare slopes AB and AC.<BR>\n" );
document.write( "They are -2 and 1/2 in that exact order.<BR>\n" );
document.write( "The slopes multiply to -1, so it proves lines AB and AC are perpendicular. <BR>\n" );
document.write( "They meet at a 90 degree angle.<BR>\n" );
document.write( "This in turn proves triangle ABC is a right triangle (where the 90 degree angle is at point A).\r<BR>\n" );
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document.write( "See this page<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1207909.html\">https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1207909.html</a><BR>\n" );
document.write( "for a proof as to why slopes that multiply to -1 lead to perpendicular lines.<BR>\n" );
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