document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1116014>Question 1116014</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The quadrilateral ABCD has vertices A(1,0), B(3,1), C(4,3) and D(2,2).<BR>\n" );
document.write( "a) Show that the intervals AC and BD bisect each other.<BR>\n" );
document.write( "b) What can be concluded about the type of quadrilateral ABCD? </SPAN>\n" );
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document.write( "part (a)<br><BR>\n" );
document.write( "Diagonal AC contains the points (1,0) and (4,3); the equation of the line through those two points is y = x-1.<br><BR>\n" );
document.write( "Diagonal BD contains the points (3,1) and (2,2); the equation of the line through those two points is y = -x+4.<br><BR>\n" );
document.write( "The intersection of the two diagonals is the common point on the graphs of y = x-1 and y = -x+4; that point is (2.5,1.5).<br><BR>\n" );
document.write( "The midpoints of AC and BD are also both (2.5,1.5).<br><BR>\n" );
document.write( "The intersection of the two diagonals is the midpoint of both, so the diagonals bisect each other.<br><BR>\n" );
document.write( "part (b)<br><BR>\n" );
document.write( "The fact that the diagonals bisect each other means the quadrilateral is a parallelogram.<br><BR>\n" );
document.write( "In fact, the quadrilateral is a rhombus, because the two diagonals are perpendicular to each other (the product of their slopes is -1).<br><BR>\n" );
document.write( "But we were not asked to show that the diagonals are perpendicular; only knowing that the diagonals bisect each other only tells us that the quadrilateral is a parallelogram. </SPAN>\n" );
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