document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=419349>Question 419349</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Give the best name for a quadrilateral whose vertices have the given coordinates.<BR>\n" );
document.write( "B(-3, 0) F(-2, 7) J(5, 8) N(4, 1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #293300 by </B><A HREF=/tutors/aboutme.mpl?userid=duckness73><B>duckness73(47)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=duckness73><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=duckness73><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=293300\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The answer is \"rhombus\".  Recall that the definition of a rhombus is a quadrilateral with all sides of equal length.\r<BR>\n" );
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document.write( "The length of any of these line segments = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt+%28%28a%5E2%29+%2B+%28b%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt+%28%28a%5E2%29+%2B+%28b%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where a is the difference in the y-coordinates and b is the difference in the x-coordinates.  Looking at segment FJ we find that the length =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%288+-+7%29%5E2+%2B+%285+-+%28-2%29%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%288+-+7%29%5E2+%2B+%285+-+%28-2%29%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281+%2B+49%29 ALIGN=MIDDLE  ALT=\"sqrt%281+%2B+49%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt+%2850%29 ALIGN=MIDDLE  ALT=\"sqrt+%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The length of BF = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%287+-+0%29%5E2+%2B+%28-2+-%28-3%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%287+-+0%29%5E2+%2B+%28-2+-%28-3%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2849+%2B+1%29 ALIGN=MIDDLE  ALT=\"sqrt%2849+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The length of BN = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281+-+0%29%5E2+%2B+%284+-%28-3%29%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%281+-+0%29%5E2+%2B+%284+-%28-3%29%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281+%2B+49%29 ALIGN=MIDDLE  ALT=\"sqrt%281+%2B+49%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The length of NJ = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%288+-+1%29%5E2+%2B+%285+-+4%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%288+-+1%29%5E2+%2B+%285+-+4%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2849+%2B+1%29 ALIGN=MIDDLE  ALT=\"sqrt%2849+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Since all sides are equal, we have a rhombus.\r<BR>\n" );
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document.write( "What we don't know yet is whether the rhombus is a square.  If the figure was a square, that would mean that adjacent sides would be perpendicular.  Two lines are perpendicular when their slopes are negative reciprocals of each other.  Let's examine any two adjacent sides, say FJ and NJ.  The slope of FJ = ((8 - 7)/(5 - (-2)) = 1/7.  The slope of NJ = (8 - 1)/(5 - 4) = 7/1 = 7.  Although the slopes are reciprocals, they are NOT negative reciprocals, so the lines are not perpendicular.  The figure is not a square, but it is still a rhombus.\r<BR>\n" );
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document.write( "Answer:  rhombus<BR>\n" );
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