document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=178276>Question 178276</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the distance from (2,1) to the line defined by y=-2x-5. Express as a radical or a number rounded to the nearest hundredth </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #133261 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=133261\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  find the distance from (2,1) to the line defined by y=-2x-5. Express as a radical or a number rounded to the nearest hundredth<BR>\n" );
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document.write( "Do it like this one.<BR>\n" );
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document.write( "find the distance from (6,5) to the line defined by y=-2x-8. express as radical or a number rounded to the nearest hundredth<BR>\n" );
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document.write( "Find the eqn of the line thru (6,5) perpendicular to y=-2x-8. <BR>\n" );
document.write( "All lines perpendicular to it have a slope, m, that's the inverse negative.<BR>\n" );
document.write( "y = -2x - 8 is in slope-intercept form, and its slope is -2, so we will find a line thru (6,5) with a slope of +1/2.<BR>\n" );
document.write( "y - y1 = m*(x - x1) where (x1,y1) is (6,5)<BR>\n" );
document.write( "y - 5 = (1/2)*(x - 6)<BR>\n" );
document.write( "2y - 10 = x - 6<BR>\n" );
document.write( "2y = x + 4<BR>\n" );
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document.write( "Solve the pair of eqns by subbing y into 2y = x + 4<BR>\n" );
document.write( "2y = x + 4<BR>\n" );
document.write( "2*(-2x-8) = x+4<BR>\n" );
document.write( "-4x-16 = x+4<BR>\n" );
document.write( "5x = -20<BR>\n" );
document.write( "x = -4<BR>\n" );
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document.write( "y = -2x-8 = -2*(-4)-8<BR>\n" );
document.write( "y = 0<BR>\n" );
document.write( "The lines intersect at (-4,0)<BR>\n" );
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document.write( "Now find the distance from (6,5) to (-4,0)<BR>\n" );
document.write( "s = sqrt((diff in y)^2 + (diff in x)^2)<BR>\n" );
document.write( "s = sqrt((0-5)^2 + (-4-6)^2)<BR>\n" );
document.write( "s = sqrt(25+100) = sqrt(125)<BR>\n" );
document.write( "distance =~11.2 units  </SPAN>\n" );
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