document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=234536>Question 234536</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Fin the area of a triangle whose vertices have coordinates of (0,9), (0, - 4), (5, -4). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #172936 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=172936\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "The first thing to do is plot the three points and draw the triangle so that you can see what you have to work with.\r<BR>\n" );
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document.write( "You can tell from the fact that two of the points have identical <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-coordinates that one of the sides of the triangle is a vertical line segment.  You can also see that two of the points have identical <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">-coordinates, so another side of the triangle is a horizontal line segment.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28%0D%0A500%2C+500%2C+-5%2C+10%2C+-5%2C+10%2C%0D%0Agrid%281%29%2C%0D%0Ablue%28line%280%2C9%2C0%2C-4%29%2C%0D%0Aline%280%2C9%2C5%2C-4%29%2C%0D%0Aline%280%2C-4%2C5%2C-4%29%29%2C%0D%0Agreen%28circle%280%2C9%2C.15%29%2C%0D%0Acircle%280%2C-4%2C.15%29%2C%0D%0Acircle%285%2C-4%2C.15%29%29%2C%0D%0Ared%28locate%280.4%2C9%2CA%280%2C9%29%29%2C%0D%0Alocate%280.4%2C-4.4%2CB%280%2C-4%29%29%2C%0D%0Alocate%285.4%2C-4.4%2CC%285%2C-4%29%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Having one side vertical and another side horizontal tells us that this is a right triangle.  We can say the base is either one of these two sides and the height is the other.\r<BR>\n" );
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document.write( "In order to compute the area, use the formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A_T\ =\ \frac{bh}{2}\">\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\"> is the measure of the base and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h\"> is the measure of the height.  Now all we need are those measurements.\r<BR>\n" );
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document.write( "Given the coordinates of two points you can find the distance between them using the distance formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d = sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\">\r<BR>\n" );
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document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_1,y_1\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_2,y_2\right)\"> are the coordinates of the two points.\r<BR>\n" );
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document.write( "Let's call line segment BC the base.  B has coordinates <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(0,-4\right)\"> and C has coordinates <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(5,-4\right)\">.  Substitute these values into the distance formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d_{BC} = sqrt{(0\ -\ 5)^2 + ((-4) - (-4))^2}\ =\ \sqrt{5^2+0^2}\ =\ \sqrt{25}\ =\ 5\">\r<BR>\n" );
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document.write( "hence the measure of the base is 5.\r<BR>\n" );
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document.write( "Do the same process to calculate the measure of the height, that is line segment AB.  Then use these values in the Area Formula to calculate your area.\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" );
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