document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80641>Question 80641</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Line l is the perpindicular bisector of AB, where A has coordinates (-2,3) and b has coordinates (5,4). Find the distance between the x and y intercepts of l.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57974 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=57974\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Line l is the perpendicular bisector of AB, where A has coordinates (-2,3) and b has coordinates (5,4). Find the distance between the x and y intercepts of l.\r<BR>\n" );
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document.write( "Here is the plan of attack on this problem. First find the mid-point of line AB.<BR>\n" );
document.write( "This will be the point where line 1 crosses (bisects) AB, then we will find the<BR>\n" );
document.write( "the slope (m1) of AB. From that we will find the slope (m2) of the line 1. Then,<BR>\n" );
document.write( "using the midpoint coordinates and m2 slope find the equation of line 1. Then,<BR>\n" );
document.write( "we can find the x & y intercepts of the line. Then find the distance between them.<BR>\n" );
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document.write( "Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x1%2Bx2%29%2F2 ALIGN=MIDDLE  ALT=\"%28x1%2Bx2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y1%2By2%29%2F2 ALIGN=MIDDLE  ALT=\"%28y1%2By2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "M.P (x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285-2%29%2F2 ALIGN=MIDDLE  ALT=\"%285-2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "M.P (y) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2B3%29%2F2 ALIGN=MIDDLE  ALT=\"%284%2B3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F2 ALIGN=MIDDLE  ALT=\"7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "x/y coordinates: 3/2, 7/2<BR>\n" );
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document.write( "Find the slope (m1), of AB<BR>\n" );
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document.write( "m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284+-+3%29%29%2F%28%285+-%28-2%29%29%29 ALIGN=MIDDLE  ALT=\"%28%284+-+3%29%29%2F%28%285+-%28-2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284+-+3%29%29%2F%28%285+%2B2+%29%29 ALIGN=MIDDLE  ALT=\"%28%284+-+3%29%29%2F%28%285+%2B2+%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%2F%287%29 ALIGN=MIDDLE  ALT=\"%281%29%2F%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Find the slope (m2) of the perpendicular line:<BR>\n" );
document.write( "We know the relationship of slopes of perpendicular lines is: m1*m2 = -1<BR>\n" );
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document.write( "(1/7) * m2 = -1<BR>\n" );
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document.write( "m2 = -7; multiplied both sides by 7<BR>\n" );
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document.write( "Find the equation of the line 1 using the point/slope formula; y-y1 = m(x-x1)<BR>\n" );
document.write( "m2 = -7; y1 = 7/2; x1 = 3/2<BR>\n" );
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document.write( "y - (7/2) = -7(x - (3/2))<BR>\n" );
document.write( "y - (7/2) = -7x + (21/2)<BR>\n" );
document.write( "y = -7x + (21/2) + (7/2)<BR>\n" );
document.write( "y = -7x + 28/2<BR>\n" );
document.write( "y = -7x + 14<BR>\n" );
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document.write( "We know the y intercept (x=0) will be 14<BR>\n" );
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document.write( "Find the x intercept (y=0)<BR>\n" );
document.write( "-7x + 14 = 0<BR>\n" );
document.write( "-7x = -14<BR>\n" );
document.write( "x = -14/-7<BR>\n" );
document.write( "x = +2<BR>\n" );
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document.write( "WE can find the distance between the intercepts using pythag: a^2 + b^2 = c^2<BR>\n" );
document.write( "Distance will be c:<BR>\n" );
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document.write( "c = Sqrt(2^2 + 14^2)<BR>\n" );
document.write( "c = Sqrt(4 + 196)<BR>\n" );
document.write( "c = Sqrt(200)<BR>\n" );
document.write( "c = 14.142 is the distance between the intercepts\r<BR>\n" );
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document.write( "Did this all makes sense to you, \r<BR>\n" );
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document.write( "Hope you did not get lost in the \"Heat of Battle!\"?\r<BR>\n" );
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document.write( " </SPAN>\n" );
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