document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=266118>Question 266118</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that (-1,-1), (9,4), (20,6), and (10,1) are the vertices of a rhombus, and then find the area of the rhombus. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #195544 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=195544\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we need the distance formula as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%28y2-y1%29%5E2+%2B+%28x2-x1%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%28y2-y1%29%5E2+%2B+%28x2-x1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "distance between: (-1,-1), (9,4) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%284-%28-1%29%29%5E2+%2B+%289-%28-1%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%284-%28-1%29%29%5E2+%2B+%289-%28-1%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%285%29%5E2+%2B+%2810%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%285%29%5E2+%2B+%2810%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28125%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "distance between: (9,4), (20,6) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%286-%284%29%29%5E2+%2B+%289-%2820%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%286-%284%29%29%5E2+%2B+%289-%2820%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%282%29%5E2+%2B+%28-11%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%282%29%5E2+%2B+%28-11%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28125%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "distance between: (20,6), and (10,1) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%281-%286%29%29%5E2+%2B+%2810-%2820%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%281-%286%29%29%5E2+%2B+%2810-%2820%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%28-5%29%5E2+%2B+%28-10%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%28-5%29%5E2+%2B+%28-10%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28125%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "distance between: (-1,-1), and (10,1) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%281-%28-1%29%29%5E2+%2B+%2810-%28-1%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%281-%28-1%29%29%5E2+%2B+%2810-%28-1%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%282%29%5E2+%2B+%28-11%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%282%29%5E2+%2B+%28-11%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28125%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "So we have shown we have a square with all sides equal. SInce the angles are all not 90 degrees, we have a rhombus.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "area = diagonal 1 x diagonal 2 / 2<BR>\n" );
document.write( "diagonal 1 = sqrt(21^2 + 7^2) = sqrt(490)<BR>\n" );
document.write( "diagonal 2 = sqrt(1^2 + 3^2) = sqrt(10)<BR>\n" );
document.write( "area = sqrt(490) * sqrt(10)/2 = 35 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );