document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255730>Question 255730</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could someone please help me solve the following?\r<BR>\n" );
document.write( "\n" );
document.write( "Calculate the distance from the point (-1,2) to the line x-4y+1=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187994 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=187994\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> point (-1,2) to the line x-4y+1=0<BR>\n" );
document.write( "step 1 - write equation as y = mx + b as<BR>\n" );
document.write( "(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+%281%2F4%29x++%2B+1%2F4 ALIGN=MIDDLE  ALT=\"Y+=+%281%2F4%29x++%2B+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 2 - identify the slope. <BR>\n" );
document.write( "The slope,m, is 1/4<BR>\n" );
document.write( "step 3 - find the perpendicular slope. This means the negative flip of the original slope. So,<BR>\n" );
document.write( "1/4 - - > -4/1<BR>\n" );
document.write( "step 4 - using our new slope find equation of line passing through (-1,2) using y = mx + b. We get<BR>\n" );
document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+mx+%2B+b ALIGN=MIDDLE  ALT=\"y+=+mx+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(iii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=+%28-4%29%2A%28-1%29+%2B+b ALIGN=MIDDLE  ALT=\"2+=+%28-4%29%2A%28-1%29+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(iv) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2+=+b ALIGN=MIDDLE  ALT=\"-2+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "new equation is<BR>\n" );
document.write( "(v) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-4x+-+2 ALIGN=MIDDLE  ALT=\"y+=+-4x+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 5 - set equation (i) = (v) and solve for x to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29x+%2B+1%2F4+=+-4x+-+2 ALIGN=MIDDLE  ALT=\"%281%2F4%29x+%2B+1%2F4+=+-4x+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply by 4 to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+1+=+-16x+-+8 ALIGN=MIDDLE  ALT=\"x+%2B+1+=+-16x+-+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17x+=+-9 ALIGN=MIDDLE  ALT=\"17x+=+-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-9%2F17 ALIGN=MIDDLE  ALT=\"x+=+-9%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 6 find y. We get Y = 2/17<BR>\n" );
document.write( "which is the crossing point at (-9/17, 2/17)<BR>\n" );
document.write( "step 7 find distance between (-1,2) and (-9/17, 2/17)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%28y2-y1%29%5E2+%2B+%28x2-x1%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%28y2-y1%29%5E2+%2B+%28x2-x1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%282%2F17-2%29%5E2+%2B+%28-9%2F17-1%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%282%2F17-2%29%5E2+%2B+%28-9%2F17-1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%283.543+%2B+2.3391%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%283.543+%2B+2.3391%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+2.425 ALIGN=MIDDLE  ALT=\"d+=+2.425\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );