document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147055>Question 147055</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the shortest distance between the parallel lines with equations 5x-12y+33=0 and 5x-12y-6=0 \r<BR>\n" );
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document.write( "PLEASE HELP!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107380 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=107380\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The answer to this problem is 3, not 3.25<BR>\n" );
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document.write( "The shortest distance between the parallel lines is the length of the perpendicular<BR>\n" );
document.write( "between the two lines, not the distance between the two intercepts on the y-axis.<BR>\n" );
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document.write( "Do it this way:<BR>\n" );
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document.write( "(1) Convert the two equations to slope intercept form.  When you do, you will get:<BR>\n" );
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document.write( "y = (5/12)x + (33/12) and<BR>\n" );
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document.write( "y = (5/12)x - (6/12)<BR>\n" );
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document.write( "Since the perpendicular to a line has a slope that is the negative inverse of the slope<BR>\n" );
document.write( "of the given line, the first slope intercept equation has a perpendicular of the form:<BR>\n" );
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document.write( "y = (-12/5)x + (+33/12)<BR>\n" );
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document.write( "and it also crosses the y-axis at the point (0, 33/12)<BR>\n" );
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document.write( "The question then becomes at what point does this perpendicular line cross the second<BR>\n" );
document.write( "given line.  Find this by simultaneously solving the second equation and the perpendicular<BR>\n" );
document.write( "equation. In other words solve the equation pair:<BR>\n" );
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document.write( "y = (5/12)x - (6/12) and<BR>\n" );
document.write( "y = (-12/5)x + (33/12)<BR>\n" );
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document.write( "You should find that the common solution of this pair is the coordinate point (15/13, -1/52)<BR>\n" );
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document.write( "Now you have the two critical points where the perpendicular crosses both of the graphs <BR>\n" );
document.write( "of the original equations. The graph of what you have is shown below:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-3%2C3%2C-3%2C3%2C%285%2F12%29x+%2B%2833%2F12%29%2C%285%2F12%29x-%286%2F12%29%2C%28-12%2F5%29x%2B%2833%2F12%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The point where the purple perpendicular line crosses the red graph is (0,33/12) and<BR>\n" );
document.write( "where it crosses the green line is (15/13, -1/52).<BR>\n" );
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document.write( "Now just use the distance formula to calculate the distance between these two points, and<BR>\n" );
document.write( "you will find that the answer is 3.<BR>\n" );
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document.write( "Hope this clarifies things for you.<BR>\n" );
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document.write( " </SPAN>\n" );
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