document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1160710>Question 1160710</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that triangle ABC is right-angled using analytic geometry. Here are the coordinate points of the triangle. (0,0) and (-12,16) and (8.6). I have already managed to calculate it by solving the distance of each triangle, however, I recently learned that I must calculate the slope to answer this question and I am confused!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #784096 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=784096\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "For easier reference, label the three points<BR>\n" );
document.write( "A = (0,0)<BR>\n" );
document.write( "B = (-12,16)<BR>\n" );
document.write( "C = (8,6)<BR>\n" );
document.write( "It doesn't matter which letters you use, or what order you go with.\r<BR>\n" );
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document.write( "Let's find the slope of the line through points A and B<BR>\n" );
document.write( "Use the slope formula<BR>\n" );
document.write( "m = (y2-y1)/(x2-x1)<BR>\n" );
document.write( "m = (16-0)/(-12-0)<BR>\n" );
document.write( "m = 16/(-12)<BR>\n" );
document.write( "m = -4/3<BR>\n" );
document.write( "The slope of line AB is -4/3\r<BR>\n" );
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document.write( "Repeat for the slope of line BC<BR>\n" );
document.write( "m = (y2-y1)/(x2-x1)<BR>\n" );
document.write( "m = (6-16)/(8-(-12))<BR>\n" );
document.write( "m = (6-16)/(8+12)<BR>\n" );
document.write( "m = -10/20<BR>\n" );
document.write( "m = -1/2<BR>\n" );
document.write( "The slope of line BC is -1/2\r<BR>\n" );
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document.write( "Finally, compute the slope of line AC<BR>\n" );
document.write( "m = (y2-y1)/(x2-x1)<BR>\n" );
document.write( "m = (6-0)/(8-0)<BR>\n" );
document.write( "m = 6/8<BR>\n" );
document.write( "m = 3/4\r<BR>\n" );
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document.write( "----------------------------------------------<BR>\n" );
document.write( "Recapping everything so far, we found these three slopes<BR>\n" );
document.write( "slope of AB = -4/3<BR>\n" );
document.write( "slope of BC = -1/2<BR>\n" );
document.write( "slope of AC = 3/4\r<BR>\n" );
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document.write( "Now multiply each slope with one another<BR>\n" );
document.write( "(slope AB)*(slope BC) = (-4/3)*(-1/2) = 2/3<BR>\n" );
document.write( "(slope AB)*(slope AC) = (-4/3)*(3/4) = -12/12 = -1<BR>\n" );
document.write( "(slope BC)*(slope AC) = (-1/2)*(3/4) = -3/8\r<BR>\n" );
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document.write( "The result in which we got -1 as a product is what we're after here. If two lines have their slopes multiply to -1, then those lines are perpendicular. This is assuming neither line is vertical.\r<BR>\n" );
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document.write( "The work above shows slopes AB and AC multiply to -1. They have the letter A in common. At the top of the page, I defined point A to be (0,0). This is where the 90 degree angle is located. Angle BAC, or CAB, is 90 degrees.\r<BR>\n" );
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document.write( "Diagram:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"40%\" src = \"https://i.imgur.com/JwT9BNq.png\"><BR>\n" );
document.write( "(diagram created with <a  rel=nofollow HREF= \"https://www.geogebra.org/?lang=en\">GeoGebra</a>)<BR>\n" );
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