document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197662>Question 1197662</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I have been struggling to this kind of problems can you help me? Here is the problem. Show in two ways that (-3,2), (-6,-2), (-1,-2) and (2,2) are the vertices of a rhombus.<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 #831043 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=831043\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Method 1) Show that all four sides are the same length.\r<BR>\n" );
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document.write( "Let<BR>\n" );
document.write( "A = (-3,2)<BR>\n" );
document.write( "B = (-6,-2)<BR>\n" );
document.write( "C = (-1,-2)<BR>\n" );
document.write( "D = (2,2)\r<BR>\n" );
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document.write( "Use the distance formula to find the distance from A to B; i.e. the length of segment AB.<BR>\n" );
document.write( "(x1,y1) = (-3,2) and (x2,y2) = (-6,-2)<BR>\n" );
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document.write( "Side AB is exactly 5 units long.\r<BR>\n" );
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document.write( "Repeat this set of steps to find the lengths of these three other sides:<BR>\n" );
document.write( "BC<BR>\n" );
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document.write( "You should get 5 as the result of each segment if this figure is truly a rhombus.\r<BR>\n" );
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document.write( "Method 2) Perpendicular diagonals and parallel sides.\r<BR>\n" );
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document.write( "The diagonals are AC and BD assuming the vertices are arranged in the order ABCD (clockwise or counterclockwise).\r<BR>\n" );
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document.write( "Let's find the slope of AC<BR>\n" );
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document.write( "Line AC has a slope of -2.\r<BR>\n" );
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document.write( "Now find the slope of diagonal BD<BR>\n" );
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document.write( "The slope of line BD is 1/2.\r<BR>\n" );
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document.write( "The two slopes (-2 and 1/2) multiply to -1 which shows the diagonals are perpendicular. Put another way, each slope is the negative reciprocal of one another.\r<BR>\n" );
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document.write( "Unfortunately the diagonals being perpendicular is not enough information to conclude we have a rhombus. The figure might be a kite.\r<BR>\n" );
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document.write( "The last thing we need is to show that the opposite sides AB and CD are parallel; as well as BC being parallel to AD.\r<BR>\n" );
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document.write( "Use the slope formula to find the slope of side AB<BR>\n" );
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document.write( "Now do the same for side CD.<BR>\n" );
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document.write( "We get the same result which shows that AB is parallel to CD.\r<BR>\n" );
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document.write( "I'll let you check to see if BC is parallel to AD. That's the last piece of the puzzle to complete method 2, in showing we have a rhombus.<BR>\n" );
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