document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1117365>Question 1117365</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The vertices of triangle OAB are the points O (0,0), A (0,2) and B (3,-1),<BR>\n" );
document.write( "a) The point S is on AB such that OS is perpendicular to AB. Find the coordinates of S, and show this point on your diagram.<BR>\n" );
document.write( "b) Find the area of triangle OAB.<BR>\n" );
document.write( "c) The line through the point B, perpendicular to OA, meets OS produced at T. Find the coordinates of T.<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 #732432 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=732432\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=solver91311&illustration_name=scaleneTriangleAtOrigin1.jpg\">.\r<BR>\n" );
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document.write( "Equation of the line containing the segment <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \overline{AB}\">.  Use the Two-Point Form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ 2\ =\ \frac{2\ -\ (-1)}{0\ -\ 3}(x\ -\ 0)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -x\ +\ 2\">\r<BR>\n" );
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document.write( "By inspection, the slope of this line is -1.\r<BR>\n" );
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document.write( "Since the slopes of perpendicular lines are negative reciprocals, the slope of the line containing the segment <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large OS\"> must be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{1}{-1}\ =\ 1\">\r<BR>\n" );
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document.write( "Using the Point-Slope form, the equation of the line containing the segment <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \overline{OS}\"> is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  y\ -\ 0\ =\ x\ -\ 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  y\ =\ x\">\r<BR>\n" );
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document.write( "Solving the 2X2 system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  x\ =\ -x\ +\ 2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  x\ =\ 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  y\ =\ 1\">\r<BR>\n" );
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document.write( "Hence, the point of intersection is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (1,\,1)\">\r<BR>\n" );
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document.write( "Using the distance formula, find the measures of segments<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \overline{AB}\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \overline{OS}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  AB\ =\ \sqrt{\(0\,-\,3\)^2\ +\ (2\,-\,(-1)\)^2}\ =\ \sqrt{9\ +\ 9}\ =\ 3\sqrt{2}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  OS\ =\ \sqrt{\(0\,-\,1\)^2\ +\ (0\,-\,1\)^2}\ =\ \sqrt{1\ +\ 1}\ =\ \sqrt{2}\">\r<BR>\n" );
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document.write( "The area of a triangle is given by one-half the base times the altitude:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \text{Area}_{OAS}\ =\ \frac{1}{2}\3(\sqrt{2}\)\(\sqrt{2}\)\ =\ \frac{1}{2}\,\cdot\,3\,\cdot\,2\ =\ 3\"> \r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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