document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100406>Question 1100406</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the distance  from point A(&#8722;14, 5) to the line &#8722;x+2y = 14.  Round your answer to the nearest tenth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #714883 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=714883\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "There is a beatiful formula to find the distance from the given point to the given straight line in a coordinate plane.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This formula is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "    Let the straight line in a coordinate plane is defined in terms of its linear equation \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "        a*x + b*y + c = 0,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    where &nbsp;<B>a</B>, &nbsp;<B>b</B> and &nbsp;<B>c</B> &nbsp;are real numbers, &nbsp;and let &nbsp;<B>P</B> = <B>P</B>(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B0%5D ALIGN=MIDDLE  ALT=\"x%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B0%5D ALIGN=MIDDLE  ALT=\"y%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >)&nbsp; is the point in the coordinate plane \r\n" );
document.write( "    with the coordinates &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B0%5D ALIGN=MIDDLE  ALT=\"x%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B0%5D ALIGN=MIDDLE  ALT=\"y%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >. &nbsp;Then the distance from the point &nbsp;<B>P</B>&nbsp; to the straight line is equal to\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "        d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28a%2Ax%5B0%5D+%2B+b%2Ay%5B0%5D+%2B+c%29%2Fsqrt%28a%5E2+%2B+b%5E2%29 ALIGN=MIDDLE  ALT=\"abs%28a%2Ax%5B0%5D+%2B+b%2Ay%5B0%5D+%2B+c%29%2Fsqrt%28a%5E2+%2B+b%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "See the lesson &nbsp;<A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Vectors/The-distance-from-a-point-to-a-straight-line-in-a-coordinate-plane.lesson>The distance from a point to a straight line in a coordinate plane</A>&nbsp; in this site.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So, in your case  &nbsp;a= -1, &nbsp;b= 2, &nbsp;c= -14   &nbsp;&nbsp;(after moving &nbsp;\"c\" &nbsp;from the righ side to the left), &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B0%5D ALIGN=MIDDLE  ALT=\"x%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >= -14,  &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B0%5D ALIGN=MIDDLE  ALT=\"y%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Substituting to the formula gives you the distance\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "    d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28%28-1%29%2A%28-14%29+%2B+2%2A5+-14%29%2Fsqrt%28%28-1%29%5E2%2B2%5E2%29 ALIGN=MIDDLE  ALT=\"abs%28%28-1%29%2A%28-14%29+%2B+2%2A5+-14%29%2Fsqrt%28%28-1%29%5E2%2B2%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%2814%2B10-14%29%2Fsqrt%281+%2B+4%29 ALIGN=MIDDLE  ALT=\"abs%2814%2B10-14%29%2Fsqrt%281+%2B+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Fsqrt%285%29 ALIGN=MIDDLE  ALT=\"10%2Fsqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2Asqrt%285%29%29%2F5%29 ALIGN=MIDDLE  ALT=\"%2810%2Asqrt%285%29%29%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4.5 (approximately; rounded to the nearest tenth).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solved.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Again, &nbsp;for the proof of the formula and other details look into the above referred lesson.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );