document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205592>Question 205592</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Point A (-4,1) is in the standard (x,y) coordinate plane.  What must be the coordinates of point B so that the line x=2 is the perpendicular bisector of AB? (with a line above the AB - what does that mean?) The answer is (8,1). How was this answer determined?\r<BR>\n" );
document.write( "\n" );
document.write( "This is a sample question from a review of questions that I might have on a placement test to determine my math knowledge. I am going back to college for more eduation after many years away from it.\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #155226 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=155226\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, AB with a line above it is shorthand for \"line segment AB\".<BR>\n" );
document.write( "Given point A is (-4, 1).<BR>\n" );
document.write( "Now since the line segment AB is bisected by the perpendicular line x = 2, (a vertical line) then you can conclude that the midpoint of line segment AB is at the point (2, 1).<BR>\n" );
document.write( "Why, because the line segment AB is horizontal and we know this because the line x = 2 (a vertical line) is the perpendicular bisector of line segment AB, and the line x = 2 must pass through the center of the line segment AB and intersect it at the point (2, 1).<BR>\n" );
document.write( "So, using the midpoint formula which gives us the x- and y-coordinates of the midpoint (2, 1):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5B1%5D%2Bx%5B2%5D%29%2F2%29 ALIGN=MIDDLE  ALT=\"%28%28x%5B1%5D%2Bx%5B2%5D%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y%5B1%5D%2By%5B2%5D%29%2F2%29 ALIGN=MIDDLE  ALT=\"%28%28y%5B1%5D%2By%5B2%5D%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+-4 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+1 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > substituting, we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-4%2Bx%5B2%5D%29%2F2%29+=+2 ALIGN=MIDDLE  ALT=\"%28%28-4%2Bx%5B2%5D%29%2F2%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2By%5B2%5D%29%2F2%29+=+1 ALIGN=MIDDLE  ALT=\"%28%281%2By%5B2%5D%29%2F2%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D ALIGN=MIDDLE  ALT=\"y%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > which will be the x- and y-coordinates of point B.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%2Bx%5B2%5D%29%2F2+=+2 ALIGN=MIDDLE  ALT=\"%28-4%2Bx%5B2%5D%29%2F2+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2Bx%5B2%5D+=+4 ALIGN=MIDDLE  ALT=\"-4%2Bx%5B2%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now add 4 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5B2%5D+=+8%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5B2%5D+=+8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and for the y-coordinate of B...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2By%5B2%5D%29%2F2+=+1 ALIGN=MIDDLE  ALT=\"%281%2By%5B2%5D%29%2F2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2By%5B2%5D+=+2 ALIGN=MIDDLE  ALT=\"1%2By%5B2%5D+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y%5B2%5D+=+1%29 ALIGN=MIDDLE  ALT=\"highlight%28y%5B2%5D+=+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "The coordinates of point B are (8, 1) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );