document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=570227>Question 570227</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I've been out sick since Monday and have been getting my work sent home.  I've missed this lesson and can't for the life of me figure out how to do this.  I've got 10 other similar problems to do but should be able to figure it out if some kind soul will help me understand.\r<BR>\n" );
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document.write( "Calculate the distance from point (-2,3) to the line y=x+1\r<BR>\n" );
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document.write( "I would really, really appreciate an explanation not just an answer since I have 9 more of these :)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #367636 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=367636\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> They want the SHORTest distance from the<BR>\n" );
document.write( "point to the line. There are lots of lines you<BR>\n" );
document.write( "could draw from the point to the line, but<BR>\n" );
document.write( "only 1 is the shortest.<BR>\n" );
document.write( "That shortest distance is the perpendicular<BR>\n" );
document.write( "from the point to the line.<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "The 1st thing to do is find the slope of the line.<BR>\n" );
document.write( "Get it into the form <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;\" > where <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+ ALIGN=MIDDLE  ALT=\"+m+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slope. ( It's already in that form )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+x+%2B+1+ ALIGN=MIDDLE  ALT=\"+y+=+x+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > The slope 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" );
document.write( "------------------------<BR>\n" );
document.write( "Now you want the slope of ANY line which would<BR>\n" );
document.write( "be perpendicular to this line.<BR>\n" );
document.write( "That formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-%28+1%2Fm+%29+=+-%281%2F1%29+ ALIGN=MIDDLE  ALT=\"+-%28+1%2Fm+%29+=+-%281%2F1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "so the perpendicular will have slope = <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" );
document.write( "------------------------<BR>\n" );
document.write( "Now you have the point (-2,3) and a slope. Use<BR>\n" );
document.write( "the point-slope formula to get the equation of<BR>\n" );
document.write( "the perpendicular line.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+y+-+3+%29+%2F+%28+x+-%28-2%29+%29+=+-1+ ALIGN=MIDDLE  ALT=\"+%28+y+-+3+%29+%2F+%28+x+-%28-2%29+%29+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+-+3+=+-1%2A%28+x+%2B+2+%29+ ALIGN=MIDDLE  ALT=\"+y+-+3+=+-1%2A%28+x+%2B+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-x+-+2+%2B+3+ ALIGN=MIDDLE  ALT=\"+y+=+-x+-+2+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-x+%2B+1+ ALIGN=MIDDLE  ALT=\"+y+=+-x+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Now where do these 2 lines intersect?<BR>\n" );
document.write( "Add the equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+x+%2B+1+ ALIGN=MIDDLE  ALT=\"+y+=+x+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-x+%2B+1+ ALIGN=MIDDLE  ALT=\"+y+=+-x+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y+=+2+ ALIGN=MIDDLE  ALT=\"+2y+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+1+ ALIGN=MIDDLE  ALT=\"+y+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+x+%2B+1+ ALIGN=MIDDLE  ALT=\"+y+=+x+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+=+x+%2B+1+ ALIGN=MIDDLE  ALT=\"+1+=+x+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+0+ ALIGN=MIDDLE  ALT=\"+x+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So now you have 2 points, (-2,3) and (0,1)<BR>\n" );
document.write( "The formula for distance is<BR>\n" );
document.write( "distance = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+%28+-2+-+0%29%5E2+%2B+%28+3+-+1+%29%5E2+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+%28+-2+-+0%29%5E2+%2B+%28+3+-+1+%29%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "distance = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+%28-2%29%5E2+%2B+2%5E2+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+%28-2%29%5E2+%2B+2%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "distance = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+4+%2B+4+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+4+%2B+4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "distance = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2Asqrt%282%29+ ALIGN=MIDDLE  ALT=\"+2%2Asqrt%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Here's a plot of the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+x+%2B+1+ ALIGN=MIDDLE  ALT=\"+y+=+x+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the line<BR>\n" );
document.write( "perpendicular to it going through (-2,3)<BR>\n" );
document.write( "The intersection is at (0,1) as you can see<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+x+%2B+1%2C+-x+%2B+1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+x+%2B+1%2C+-x+%2B+1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );