document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135980>Question 135980</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to establish the correct equation for\r<BR>\n" );
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document.write( "The points (1,5), (4,5), and (1,0) represent three corners of a rectangle; find the coordinates of the fourth point.\r<BR>\n" );
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document.write( "For obvious reasons I concluded that the fourth point is (4,0), but I am unsure how to present this.\r<BR>\n" );
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document.write( "m = y4 - y3 – y2 – y1/x4 - x3 – x2 – x1\r<BR>\n" );
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document.write( "m = 5 – 5 – 0 – 5/1 – 4 – 1 – 4\r<BR>\n" );
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document.write( "Thanks!\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99611 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=99611\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since you have three vertices of the rectangle, you have two sides defined, namely the line segment from (1,5) to (4,5) and the line segment from (1,5) to (1,0).  The segment from (1,5) to (4,5) must be parallel to the segment between (1,0) and your missing point (x,y), and the segment from (1,5) to (1,0) must be parallel to the segment between (4,5) and your missing point (x,y).\r<BR>\n" );
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document.write( "Since the y coordinates of (1,5) and (4,5) are equal, the equation for the line containing the line segment connecting these two points must be the equation of a horizontal line, namely <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5 ALIGN=MIDDLE  ALT=\"y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Since the segment between (1,0) and (x,y) is parallel to this line, it must be a horizontal line as well, and since the y-coordinate of one of the points is 0, all of the y-coordinates must be 0 and the equation must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Using similar logic, the equation for the segment from (1,5) to (1,0) must be <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;\" > and therefore the equation for the segment from (4,5) to (x,y) must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Hence your point is the intersection of the two lines represented by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the ordered pair is the solution set of the system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Which is (4,0) </SPAN>\n" );
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