document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=749634>Question 749634</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the distance from (6,-4) to the line defined by y=2x-6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #456129 by </B><A HREF=/tutors/aboutme.mpl?userid=tommyt3rd><B>tommyt3rd(5050)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tommyt3rd><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=tommyt3rd><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=456129\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Typically we ask for the shortest distance because the distance from the line varies. So here we go...\r<BR>\n" );
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document.write( "There is a line perpendicular to our line that passes through (6,-4). Since it is perpendicular it has the slope -1/2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Agraph%28300%2C300%2C-10%2C10%2C-10%2C10%2C2%2Ax-6%2C2%2Ax-16%2C-.5%2Ax-1%29%0D%0A ALIGN=MIDDLE  ALT=\"%0D%0Agraph%28300%2C300%2C-10%2C10%2C-10%2C10%2C2%2Ax-6%2C2%2Ax-16%2C-.5%2Ax-1%29%0D%0A\"   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=%0D%0Ay-%28-4%29=%28-1%2F2%29%28x-6%29%0D%0A ALIGN=MIDDLE  ALT=\"%0D%0Ay-%28-4%29=%28-1%2F2%29%28x-6%29%0D%0A\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "After some simplifying we can get\r<BR>\n" );
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document.write( "Notice that this new line must intersect our original at a point exactly parallel to (6,-4)  (why?)\r<BR>\n" );
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document.write( "Therefore if we find the point of intersection we can use that point to find our distance\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-6=%28-1%2F2%29x-1 ALIGN=MIDDLE  ALT=\"y=2x-6=%28-1%2F2%29x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and this leads us to the x-coordinate which is  x=2 and so y=2(2)-6=-2\r<BR>\n" );
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document.write( "Next we find the distance between (6,-4) and (2,-2)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%286-2%29%5E2%2B%28-4-%28-2%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%286-2%29%5E2%2B%28-4-%28-2%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and this gives us \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=2sqrt%285%29%0D%0A ALIGN=MIDDLE  ALT=\"d=2sqrt%285%29%0D%0A\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Actually in precalculus there is a formula:\r<BR>\n" );
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document.write( ":) </SPAN>\n" );
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