document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085416>Question 1085416</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the line UV has equation 5x-2y=7.the point U has coordinates (1,-1) and the point V has coordinates (3,r),find in general form ,the equation of the perpendicular bisector of UV </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699528 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=699528\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solving for y, UV has the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%285%2F2%29x+-+7%2F2+ ALIGN=MIDDLE  ALT=\"+y+=+%285%2F2%29x+-+7%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Using the above, we can plug in x=3 in order to find r:\r<BR>\n" );
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document.write( "       y = (5/2)(3) - 7/2 <BR>\n" );
document.write( "       y = 15/2 - 7/2 = 8/2 = 4\r<BR>\n" );
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document.write( "So r=4, or equivalently, V is at (3,4).\r<BR>\n" );
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document.write( "Let the line MN be the perpendicular bisector of UV, and let M be the midpoint of UV.\r<BR>\n" );
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document.write( "Line MN has slope -2/5   (for y=mx+b, a line perpendicular Y=MX+B  will always have slope M=-1/m).<BR>\n" );
document.write( "So far for MN we have  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y++=+-%282%2F5%29x+%2B+b+ ALIGN=MIDDLE  ALT=\"+y++=+-%282%2F5%29x+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We just need b.  <BR>\n" );
document.write( "To find b, we need M:   M is at the midpoint of UV:  ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283%2B1%29%2F2+ ALIGN=MIDDLE  ALT=\"+%283%2B1%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%284+%2B+%28-1%29%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+%284+%2B+%28-1%29%29+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > )  or <BR>\n" );
document.write( "( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+ ALIGN=MIDDLE  ALT=\"+2+\"   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;\" > )\r<BR>\n" );
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document.write( "Now  plug in x & y and solve for b:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2F2+=+%28-2%2F5%29%282%29+%2B+b+ ALIGN=MIDDLE  ALT=\"+3%2F2+=+%28-2%2F5%29%282%29+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > —> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+3%2F2+%2B+4%2F5+=+15%2F10+%2B+8%2F10+=+23%2F10+ ALIGN=MIDDLE  ALT=\"+b+=+3%2F2+%2B+4%2F5+=+15%2F10+%2B+8%2F10+=+23%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "—\r<BR>\n" );
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document.write( "Ans:  The perpendicular bisector of UV has equation  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight_green%28y+=+%28-2%2F5%29x+%2B+23%2F10%29+ ALIGN=MIDDLE  ALT=\"+highlight_green%28y+=+%28-2%2F5%29x+%2B+23%2F10%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( " </SPAN>\n" );
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