document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=804862>Question 804862</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the shortest distance from the point D(5,4) to the line represented by 3x+5y-4=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #484987 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=484987\">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( "The shortest distance from a point to a line is the distance between the given point and the point of intersection of the line perpendicular to the given line and passing through the given point.\r<BR>\n" );
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document.write( "Step 1:  Determine the slope of the line represented by the given equation (hereinafter referred to as the given line).\r<BR>\n" );
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document.write( "Step 2:  Calculate the slope of a perpendicular to the given line by taking the negative reciprocal of the slope of the given line.\r<BR>\n" );
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document.write( "Step 3:  Use the point-slope form, the coordinates of point D, and the slope calculated in step 2 to derive an equation of the line perpendicular to the given line that passes through point D.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ y_1\ =\ m(x\ -\ x_1) \">\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)\"> are the coordinates of the given point and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large m\"> is the calculated slope.\r<BR>\n" );
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document.write( "Step 4:  Solve the 2X2 linear system consisting of the given equation and the equation derived in step 3.\r<BR>\n" );
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document.write( "Step 5:  Use the distance formula to calculate the distance between point D and the point of intersection represented by the coordinates of the ordered pair that is the solution set from step 4.\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 given (or derived) points.\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( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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