document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185691>Question 1185691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that point A is (-2,4), C (4,7), and B (2,-2), what is the shortest distance from B to AC? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816554 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=816554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The solution method shown by the other tutor is fine.<br><BR>\n" );
document.write( "Here is an alternative method.  If you are solving this kind of problem (finding the shortest distance from a point to a line) frequently, this method will be faster.<br><BR>\n" );
document.write( "(1) Find the equation of line AC in the form Ax+By+C=0.<br><BR>\n" );
document.write( "From A to C the change in x is +6 and the change in y is +3, so the slope is 3/6 = 1/2.  So the equation is of the form y=(1/2)x+b.<BR>\n" );
document.write( "Plug in either of the given (x,y) values to determine b.<BR>\n" );
document.write( "4=(1/2)(-2)+b<BR>\n" );
document.write( "4=-1+b<BR>\n" );
document.write( "b=5<br><BR>\n" );
document.write( "The equation of the line in slope-intercept form is y=(1/2)x+5.<br><BR>\n" );
document.write( "Put the equation in the required form.<br><BR>\n" );
document.write( "y=(1/2)x+5<BR>\n" );
document.write( "2y=x+10<BR>\n" );
document.write( "x-2y+10=0<br><BR>\n" );
document.write( "(2) Use the formula for the (shortest) distance from a point (p,q) to the line with equation Ax+By+C=0:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28%28Ap%2BBq%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29%29 ALIGN=MIDDLE  ALT=\"abs%28%28Ap%2BBq%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28%281%282%29%2B%28-2%29%28-2%29%2B10%29%2Fsqrt%281%5E2%2B2%5E2%29%29+=+abs%2816%2Fsqrt%285%29%29+=+16%2Fsqrt%285%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 7.1554 to 4 decimal places<br>\r<BR>\n" );
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