document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=317624>Question 317624</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the point on the line y = 2x - 5 that is nearest the origin.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " a. (2 , -1)\r<BR>\n" );
document.write( "\n" );
document.write( " b. (1 , 2)\r<BR>\n" );
document.write( "\n" );
document.write( " c. (2 , 2)\r<BR>\n" );
document.write( "\n" );
document.write( " d. (-1 , 1)\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #227448 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=227448\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the point on the line y = 2x - 5 that is nearest the origin. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a. (2 , -1) <BR>\n" );
document.write( "b. (1 , 2) <BR>\n" );
document.write( "c. (2 , 2) <BR>\n" );
document.write( "d. (-1 , 1) <BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "The shortest distance from the origin to the line is perpendicular to the line.<BR>\n" );
document.write( "The slope of y = 2x - 5 is 2.<BR>\n" );
document.write( "The slope of lines perpendicular have a slope that's the negative inverse, <BR>\n" );
document.write( "m = -1/2.<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Use y = mx + b and the point (0,0) --> y = (-1/2)x<BR>\n" );
document.write( "Find where y = -x/2 intersects y = 2x - 5<BR>\n" );
document.write( "-x/2 = 2x - 5<BR>\n" );
document.write( "-x = 4x - 10<BR>\n" );
document.write( "-5x = -10<BR>\n" );
document.write( "x = 2<BR>\n" );
document.write( "y = -1<BR>\n" );
document.write( "--> the point (2,-1) nearest the origin<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Tho is wasn't asked for:<BR>\n" );
document.write( "The distance from the origin is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%282%5E2+%2B+1%29+=+sqrt%285%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%282%5E2+%2B+1%29+=+sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );