document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131976>Question 1131976</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The coordinates of the vertices of parallelogram ABCD are A(-1,-3), B(7,2), C(5,8), D(-3,3). Using the diagonals, determine whether ABCD is a rhombus. Show all your work and state appropriate formulas and theorems used. </SPAN>\n" );
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document.write( "Note even a very rough sketch of the four given points, without doing any calculations, suggests that the figure might be a parallelogram or even a rectangle, but not a rhombus.<br><BR>\n" );
document.write( "For ABCD to be a rhombus, we must have all three of the following:<br><BR>\n" );
document.write( "(1) AB parallel to CD (slopes the same)<BR>\n" );
document.write( "(2) BC parallel to AD (slopes the same)<BR>\n" );
document.write( "(3) AC perpendicular to BD (product of slopes is -1)<br><BR>\n" );
document.write( "If any ONE of these is not satisfied, the figure is not a rhombus.<br><BR>\n" );
document.write( "(1) slope of AB: 5/8; slope of CD: 5/8 -- okay<BR>\n" );
document.write( "(2) slope of BC: 6/2 = 3; slope of AD: 6/2 = 3 -- okay<BR>\n" );
document.write( "(3) slope of AC: 11/6; slope of BD: -1/10 -- NOT okay<br><BR>\n" );
document.write( "The figure is indeed a parallelogram, because opposite pairs of sides are parallel.  But the slopes of the diagonals are not perpendicular.<br><BR>\n" );
document.write( "ANSWER: The figure is not a rhombus, because the diagonals are not perpendicular. </SPAN>\n" );
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