document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147056>Question 147056</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i have a question if my multiple choice answers for my question <BR>\n" );
document.write( "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( "A.3<BR>\n" );
document.write( "B.39<BR>\n" );
document.write( "C.27/5<BR>\n" );
document.write( "D.27/13<BR>\n" );
document.write( "E.N/a\r<BR>\n" );
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document.write( "how did u come up with the answer 3.25<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 #107382 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=107382\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-12y%2B33=0 ALIGN=MIDDLE  ALT=\"5x-12y%2B33=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12y%2B33=0-5x ALIGN=MIDDLE  ALT=\"-12y%2B33=0-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x ALIGN=MIDDLE  ALT=\"5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12y=0-5x-33 ALIGN=MIDDLE  ALT=\"-12y=0-5x-33\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33 ALIGN=MIDDLE  ALT=\"33\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12y=-5x-33 ALIGN=MIDDLE  ALT=\"-12y=-5x-33\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5x-33%29%2F%28-12%29 ALIGN=MIDDLE  ALT=\"y=%28-5x-33%29%2F%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12 ALIGN=MIDDLE  ALT=\"-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F12%29x%2B11%2F4 ALIGN=MIDDLE  ALT=\"y=%285%2F12%29x%2B11%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "-----------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-12y-6=0 ALIGN=MIDDLE  ALT=\"5x-12y-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now move onto the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12y-6=0-5x ALIGN=MIDDLE  ALT=\"-12y-6=0-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x ALIGN=MIDDLE  ALT=\"5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12y=0-5x%2B6 ALIGN=MIDDLE  ALT=\"-12y=0-5x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12y=-5x%2B6 ALIGN=MIDDLE  ALT=\"-12y=-5x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5x%2B6%29%2F%28-12%29 ALIGN=MIDDLE  ALT=\"y=%28-5x%2B6%29%2F%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12 ALIGN=MIDDLE  ALT=\"-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F12%29x-1%2F2 ALIGN=MIDDLE  ALT=\"y=%285%2F12%29x-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "So when we graph the two equations, we get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%285%2F12%29x%2B11%2F4%2C+%285%2F12%29x-1%2F2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F12%29x%2B11%2F4 ALIGN=MIDDLE  ALT=\"y=%285%2F12%29x%2B11%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F12%29x-1%2F2 ALIGN=MIDDLE  ALT=\"y=%285%2F12%29x-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green)\r<BR>\n" );
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document.write( "Notice how the slope of the two equations is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=5%2F12 ALIGN=MIDDLE  ALT=\"m=5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the perpendicular slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12%2F5 ALIGN=MIDDLE  ALT=\"-12%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now simply draw any perpendicular line to the equations. I'm going to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%2812%2F5%29x ALIGN=MIDDLE  ALT=\"y=-%2812%2F5%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%285%2F12%29x%2B11%2F4%2C+%285%2F12%29x-1%2F2%2C-%2812%2F5%29x%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F12%29x%2B11%2F4 ALIGN=MIDDLE  ALT=\"y=%285%2F12%29x%2B11%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F12%29x-1%2F2 ALIGN=MIDDLE  ALT=\"y=%285%2F12%29x-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green), and the perpendicular line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%2812%2F5%29x ALIGN=MIDDLE  ALT=\"y=-%2812%2F5%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > (blue)\r<BR>\n" );
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document.write( "Now use any method to find the two intersections. I used a graphing utility to get the two intersections at the points <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-\frac{165}{169},\frac{396}{169}\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(\frac{30}{169},-\frac{72}{169}\right)\">\r<BR>\n" );
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document.write( "Now let's find the distance between the two points. This distance will be the same as the shortest distance between the two lines\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the distance formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%28-165%2F169-30%2F169%29%5E2%2B%28396%2F169--72%2F169%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%28-165%2F169-30%2F169%29%5E2%2B%28396%2F169--72%2F169%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=-165%2F169 ALIGN=MIDDLE  ALT=\"x%5B1%5D=-165%2F169\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=30%2F169 ALIGN=MIDDLE  ALT=\"x%5B2%5D=30%2F169\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=396%2F169 ALIGN=MIDDLE  ALT=\"y%5B1%5D=396%2F169\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D=-72%2F169 ALIGN=MIDDLE  ALT=\"y%5B2%5D=-72%2F169\"   DISABLED_style= \"max-width:90%; height:auto;\" >. These are the coordinates of the intersections.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%28-15%2F13%29%5E2%2B%28396%2F169--72%2F169%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%28-15%2F13%29%5E2%2B%28396%2F169--72%2F169%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F169 ALIGN=MIDDLE  ALT=\"30%2F169\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-165%2F169 ALIGN=MIDDLE  ALT=\"-165%2F169\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15%2F13 ALIGN=MIDDLE  ALT=\"-15%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%28-15%2F13%29%5E2%2B%2836%2F13%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%28-15%2F13%29%5E2%2B%2836%2F13%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-72%2F169 ALIGN=MIDDLE  ALT=\"-72%2F169\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=396%2F169 ALIGN=MIDDLE  ALT=\"396%2F169\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2F13 ALIGN=MIDDLE  ALT=\"36%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28225%2F169%2B%2836%2F13%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28225%2F169%2B%2836%2F13%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15%2F13 ALIGN=MIDDLE  ALT=\"-15%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=225%2F169 ALIGN=MIDDLE  ALT=\"225%2F169\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28225%2F169%2B1296%2F169%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28225%2F169%2B1296%2F169%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2F13 ALIGN=MIDDLE  ALT=\"36%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1296%2F169 ALIGN=MIDDLE  ALT=\"1296%2F169\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%289%29 ALIGN=MIDDLE  ALT=\"d=sqrt%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=225%2F169 ALIGN=MIDDLE  ALT=\"225%2F169\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1296%2F169 ALIGN=MIDDLE  ALT=\"1296%2F169\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=3 ALIGN=MIDDLE  ALT=\"d=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=3 ALIGN=MIDDLE  ALT=\"d=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So the distance between the two points is  3 units. \r<BR>\n" );
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document.write( "So this means that the shortest distance between the two lines is also 3 units.\r<BR>\n" );
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document.write( "So the answer choice is A)\r<BR>\n" );
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