document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1116921>Question 1116921</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The perpendicular bisector of the interval CD has equation 4x-3y+16=0. C has coordinates (-9,10). find the coordinates of D </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #731860 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=731860\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A PICTURE IS USUALLY HELPFUL:<BR>\n" );
document.write( "The line with equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-3y%2B16=0 ALIGN=MIDDLE  ALT=\"4x-3y%2B16=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F3%29x%2B16%2F3 ALIGN=MIDDLE  ALT=\"y=%284%2F3%29x%2B16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > has slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "It is easy to see that it passes through point(-4,0).<BR>\n" );
document.write( "I can plot points of that line by adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the x-coordinate<BR>\n" );
document.write( "(moving 3 spaces to the right),<BR>\n" );
document.write( "and adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the y-coordinate<BR>\n" );
document.write( "(moving 4 spaces up) from any point on the line, including point (-4,0).<BR>\n" );
document.write( "That allows me to graph that line, along with point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28-9%2C10%29 ALIGN=MIDDLE  ALT=\"C%28-9%2C10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-11%2C9%2C-4%2C16%2C+grid%281%29%2C%0D%0Ared%28circle%28-9%2C10%2C0.3%29%29%2Cblue%28circle%28-4%2C0%2C0.3%29%29%2C%0D%0Ablue%28circle%28-1%2C4%2C0.3%29%29%2Cblue%28circle%282%2C8%2C0.3%29%29%2C%0D%0Ablue%28circle%285%2C12%2C0.3%29%29%2Cblue%28line%28-7%2C-4%2C8%2C16%29%29%2C%0D%0Alocate%28-9.8%2C10%2Cred%28C%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "As the line with equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-3y%2B16=0 ALIGN=MIDDLE  ALT=\"4x-3y%2B16=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F3%29x%2B16%2F3 ALIGN=MIDDLE  ALT=\"y=%284%2F3%29x%2B16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "as it is the perpendicular bisector of segment CD,<BR>\n" );
document.write( "it is perpendicular to the line CD containing segment CD, and points C and D.<BR>\n" );
document.write( "Perpendicular lines have slopes whose product is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the line containing points C and D is such that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%284%2F3%29=-1 ALIGN=MIDDLE  ALT=\"m%284%2F3%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28-1%29%283%2F4%29=-3%2F4 ALIGN=MIDDLE  ALT=\"m=%28-1%29%283%2F4%29=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That slope would allow me to plot points of line CD (and graph line CD),<BR>\n" );
document.write( "by adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the x-coordinate<BR>\n" );
document.write( "(moving 4 spaces to the right),<BR>\n" );
document.write( "and adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the y-coordinate<BR>\n" );
document.write( "(moving 3 spaces down) from any point on the line, including point C(-9,10).<BR>\n" );
document.write( "The points added and line CD are shown in green below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-11%2C9%2C-4%2C16%2C+grid%281%29%2C%0D%0Ared%28circle%28-9%2C10%2C0.3%29%29%2Cblue%28circle%28-4%2C0%2C0.3%29%29%2C%0D%0Ablue%28circle%28-1%2C4%2C0.3%29%29%2Cblue%28circle%282%2C8%2C0.3%29%29%2C%0D%0Ablue%28circle%285%2C12%2C0.3%29%29%2Cblue%28line%28-7%2C-4%2C8%2C16%29%29%2C%0D%0Agreen%28circle%28-5%2C7%2C0.4%29%29%2Cgreen%28circle%28-1%2C4%2C0.4%29%29%2C%0D%0Agreen%28circle%283%2C1%2C0.4%29%29%2Cgreen%28circle%287%2C-2%2C0.4%29%29%2C%0D%0Agreen%28line%28-13%2C13%2C11%2C-5%29%29%2Clocate%28-9.8%2C10%2Cred%28C%29%29%2C%0D%0Alocate%286.2%2C-2%2Cgreen%28D%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "From point to point on each line, I moved<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > units in one direction and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > perpendicular to that direction,<BR>\n" );
document.write( "for a distance (along the line) of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%5E2%2B4%5E2%29=5 ALIGN=MIDDLE  ALT=\"sqrt%283%5E2%2B4%5E2%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so I see that point C is at a distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the blue perpendicular bisector line,<BR>\n" );
document.write( "so the point at distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the other side of that line is point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28D%287%2C-2%29%29 ALIGN=MIDDLE  ALT=\"highlight%28D%287%2C-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . <BR>\n" );
document.write( " <BR>\n" );
document.write( "PROBABLY \"FORMULAS\" AND EQUATIONS ARE EXPECTED TO BE SHOWN:<BR>\n" );
document.write( "The line with equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-3y%2B16=0 ALIGN=MIDDLE  ALT=\"4x-3y%2B16=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F3%29x%2B16%2F3 ALIGN=MIDDLE  ALT=\"y=%284%2F3%29x%2B16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "As it is the perpendicular bisector of segment CD,<BR>\n" );
document.write( "it is perpendicular to the line CD containing segment CD, and points C and D.<BR>\n" );
document.write( "Perpendicular lines have slopes whose product is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the line containing points C and D is such that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%284%2F3%29=-1 ALIGN=MIDDLE  ALT=\"m%284%2F3%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28-1%29%283%2F4%29=-3%2F4 ALIGN=MIDDLE  ALT=\"m=%28-1%29%283%2F4%29=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "Knowing the coordinates of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28-9%2C10%29 ALIGN=MIDDLE  ALT=\"C%28-9%2C10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the slope of the line,<BR>\n" );
document.write( "we can write the equation of line CD in point-slope form as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-10=%28-3%2F4%29%28x-%28-9%29%29 ALIGN=MIDDLE  ALT=\"y-10=%28-3%2F4%29%28x-%28-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-10=%28-3%2F4%29%28x%2B9%29 ALIGN=MIDDLE  ALT=\"y-10=%28-3%2F4%29%28x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Multiplying both sides of the equal sign times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and rearranging, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y-40=-3x-27 ALIGN=MIDDLE  ALT=\"4y-40=-3x-27\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4y-13=0 ALIGN=MIDDLE  ALT=\"3x%2B4y-13=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "The intersection of linr CD and the perpendicular bisector of segment CD<BR>\n" );
document.write( "is the midpoint of CD, and is given by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283x%2B4y-13=0%2C4x-3y%2B16=0%29 ALIGN=MIDDLE  ALT=\"system%283x%2B4y-13=0%2C4x-3y%2B16=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Adding up the first equation times 3 plus the second times 4, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%2B25=0 ALIGN=MIDDLE  ALT=\"25x%2B25=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and substituting that into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-3y%2B16=0 ALIGN=MIDDLE  ALT=\"4x-3y%2B16=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4-3y%2B16=0 ALIGN=MIDDLE  ALT=\"-4-3y%2B16=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3y%2B12=0 ALIGN=MIDDLE  ALT=\"-3y%2B12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, the midpoint of CD, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%28x%5BM%5D%2Cy%5BM%5D%29 ALIGN=MIDDLE  ALT=\"M%28x%5BM%5D%2Cy%5BM%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BM%5D=-1 ALIGN=MIDDLE  ALT=\"x%5BM%5D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5BM%5D=4 ALIGN=MIDDLE  ALT=\"y%5BM%5D=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The coordinates of the midpoint of a segment CD, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%28x%5BC%5D%2Cy%5BC%5D%29 ALIGN=MIDDLE  ALT=\"M%28x%5BC%5D%2Cy%5BC%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%28x%5BD%5D%2Cy%5BD%5D%29 ALIGN=MIDDLE  ALT=\"M%28x%5BD%5D%2Cy%5BD%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are given by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BM%5D=%28x%5BC%5D%2Bx%5BD%5D%29%2F2 ALIGN=MIDDLE  ALT=\"x%5BM%5D=%28x%5BC%5D%2Bx%5BD%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5BM%5D=%28y%5BC%5D%2By%5BD%5D%29%2F2 ALIGN=MIDDLE  ALT=\"y%5BM%5D=%28y%5BC%5D%2By%5BD%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Substituting the known coordinates of C and M,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1=%28-9%2Bx%5BD%5D%29%2F2 ALIGN=MIDDLE  ALT=\"-1=%28-9%2Bx%5BD%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2=-9%2Bx%5BD%5D ALIGN=MIDDLE  ALT=\"-2=-9%2Bx%5BD%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5BD%5D=7%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5BD%5D=7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=%2810%2By%5BD%5D%29%2F2 ALIGN=MIDDLE  ALT=\"4=%2810%2By%5BD%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8=10%2By%5BD%5D ALIGN=MIDDLE  ALT=\"8=10%2By%5BD%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y%5BD%5D=-2%29 ALIGN=MIDDLE  ALT=\"highlight%28y%5BD%5D=-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );