document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=835033>Question 835033</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that the points a(3,4) b(3,1) and c(2,5) are the vertices of a right-angled triangle. Find the length of the perpendicular from a to bc. Ans 2.57.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #503311 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=503311\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the any 2 of the slopes of the <BR>\n" );
document.write( "3 lines which are formed by the<BR>\n" );
document.write( "3 points have the relationship:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%5B2%5D+=+-1%2Fm%5B1%5D+ ALIGN=MIDDLE  ALT=\"+m%5B2%5D+=+-1%2Fm%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then those<BR>\n" );
document.write( "2 lines are perpendicular and<BR>\n" );
document.write( "the triangle formed is a right triangle<BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "slope of ab:<BR>\n" );
document.write( "a(3,4), b(3,1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%5B1%5D+=+%28+4-1+%29+%2F+%28+3-3+%29+ ALIGN=MIDDLE  ALT=\"+m%5B1%5D+=+%28+4-1+%29+%2F+%28+3-3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%5B1%5D+=+3%2F0+ ALIGN=MIDDLE  ALT=\"+m%5B1%5D+=+3%2F0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is infinite slope, in other words,<BR>\n" );
document.write( "a vertical line<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "slope of bc:<BR>\n" );
document.write( "b(3,1), c(2,5)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%5B2%5D+=+%28+5-1+%29+%2F+%28+2-3+%29+ ALIGN=MIDDLE  ALT=\"+m%5B2%5D+=+%28+5-1+%29+%2F+%28+2-3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%5B2%5D+=+4%2F%28-1%29+ ALIGN=MIDDLE  ALT=\"+m%5B2%5D+=+4%2F%28-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%5B2%5D+=+-4+ ALIGN=MIDDLE  ALT=\"+m%5B2%5D+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "slope of ac:<BR>\n" );
document.write( "a(3,4),c(2,5)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%5B3%5D+=+%28+5-4+%29+%2F+%28+2-3+%29+ ALIGN=MIDDLE  ALT=\"+m%5B3%5D+=+%28+5-4+%29+%2F+%28+2-3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%5B3%5D+=+1%2F%28-1%29++ ALIGN=MIDDLE  ALT=\"+m%5B3%5D+=+1%2F%28-1%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%5B3%5D+=+-1+ ALIGN=MIDDLE  ALT=\"+m%5B3%5D+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "This looks like it's not a right triangle.<BR>\n" );
document.write( "Check your data, but get a 2nd opinion, too<BR>\n" );
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