document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=179956>Question 179956</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Calculate the shortest distance from the given line and point povided.\r<BR>\n" );
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document.write( "2x-y=3  (2,3)\r<BR>\n" );
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document.write( "I subtracted 2 from 2x-y=3 and got -y=-2+3,  I made them postitive and got y=1\r<BR>\n" );
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document.write( "I plugged 2 in for x then got seven, I put 2(1)-7=3 and recieved 5.      I was told this is incorrect but i dont know any other way to do it...any help would be helpful. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #134847 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=134847\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the equation of the line that passes thru (2,3) and is perpendicular to the given line<BR>\n" );
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document.write( "the slope of the perpendicular line will have a negative reciprical to the given line. 2x-y=3 --->y=2x-3 so m= for this line is 2. the slope for the perpendicular line is -1/2<BR>\n" );
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document.write( "y-3=(-1/2)(x-2)<BR>\n" );
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document.write( "y-3=(-1/2)x+1--->y=(-1/2)x+4--->x+2y=8<BR>\n" );
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document.write( "now we have to find the intersection of these two lines<BR>\n" );
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document.write( "2x-y=3....eq 1<BR>\n" );
document.write( "x+2y=8...eq 2<BR>\n" );
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document.write( "multiply eq 1 by 2 and add all terms of the equations together.<BR>\n" );
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document.write( "4x-2y=6....eq 1 revised<BR>\n" );
document.write( "x+2y=8....eq 2<BR>\n" );
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document.write( "y terms are eliminated becaue -2y+2y=0. We are left with 4x+x=14<BR>\n" );
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document.write( "5x=14<BR>\n" );
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document.write( "x=14/5<BR>\n" );
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document.write( "plug this value back into  eq 1 or 2. I chose eq 2<BR>\n" );
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document.write( "(14/5)+2y=8<BR>\n" );
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document.write( "2y=26/5:<BR>\n" );
document.write( "y=26/10=13/5<BR>\n" );
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document.write( "Now we can use the distance formula: we have point (2,3) and point (14/5,13/5)<BR>\n" );
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document.write( "distance between point (2,3) and line 2x-y=3 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C2x-3%2C%28-1%2F2%29x%2B4%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C2x-3%2C%28-1%2F2%29x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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