document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172332>Question 1172332</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the line perpendicular to 2x+3y=1 and whose distance from the origin is 7. Please include solutions if you can. Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #797348 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=797348\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Here are a few hints.\r<BR>\n" );
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document.write( "Hint 1)\r<BR>\n" );
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document.write( "Any standard linear equation of the form<BR>\n" );
document.write( "Ax+By = C<BR>\n" );
document.write( "is perpendicular to<BR>\n" );
document.write( "Bx-Ay = D\r<BR>\n" );
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document.write( "I've swapped the A and B coefficients, and made the plus sign into a minus sign. We use a new value D so that it's different from C.\r<BR>\n" );
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document.write( "In the case of 2x+3y = 1, we have<BR>\n" );
document.write( "A = 2<BR>\n" );
document.write( "B = 3<BR>\n" );
document.write( "C = 1\r<BR>\n" );
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document.write( "Anything perpendicular to 2x+3y = 1 looks like<BR>\n" );
document.write( "Bx-Ay = D<BR>\n" );
document.write( "3x-2y = D\r<BR>\n" );
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document.write( "Hint 2)\r<BR>\n" );
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document.write( "Refer to this diagram<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"50%\" src = \"https://i.imgur.com/N39kUqV.png\"><BR>\n" );
document.write( "We have the blue line as 2x+3y = 1<BR>\n" );
document.write( "The red line 2x+3y = 0 is parallel to the blue one. This red line goes through the origin, which helps us find point P.\r<BR>\n" );
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document.write( "The green line is perpendicular to the red line, and it is one of the answers. It goes through point P. Note how point P is 7 units away from the center point O. <BR>\n" );
document.write( "Segment OP = 7 units<BR>\n" );
document.write( "Similarly, OQ = 7 units as well.\r<BR>\n" );
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document.write( "You'll have to use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=49 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=49\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3y=0 ALIGN=MIDDLE  ALT=\"2x%2B3y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to determine the coordinates of P and Q. So you'll get two possible answers. Once you know the coordinates of P, you plug them into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y=D ALIGN=MIDDLE  ALT=\"3x-2y=D\"   DISABLED_style= \"max-width:90%; height:auto;\" > to determine the value of D. Do the same for the coordinates of Q\r<BR>\n" );
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document.write( "Note: the diagram above shows only one of the two solutions. The other solution is the same idea but it goes through Q instead. <BR>\n" );
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