document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113923>Question 113923</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi. How would I use the distance, midpoint and slope formula to find where a point should go to make a parallelogram? Because on this homework it shows point A(7,12) B(15,4) C(9,2) D(3,5) The question is to move Point B so that it makes a parallelogram. How would I know where to move it? Thank You for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82912 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=82912\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How would I use the distance, midpoint and slope formula to find where a point should go to make a parallelogram? Because on this homework it shows point A(7,12) B(15,4) C(9,2) D(3,5) The question is to move Point B so that it makes a parallelogram. How would I know where to move it? Thank You for your help!<BR>\n" );
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document.write( "Plot the points A, C, and D.<BR>\n" );
document.write( "AB has to be parallel to DC.<BR>\n" );
document.write( "The slope of DC = (2-5)/(9-3) = -3/6 = -1/2<BR>\n" );
document.write( "So the slope of AB as to be -1/2.<BR>\n" );
document.write( "AB also has to pass thru A(7,12)<BR>\n" );
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document.write( "Line AB has the form y=mx+b where y = 12 when x=7, and m = -1/2<BR>\n" );
document.write( "12 = (-1/2)7 + b<BR>\n" );
document.write( "b = 24/2 +7/2 = 31/2<BR>\n" );
document.write( "AB has equation y = (-1/2)x+31/2<BR>\n" );
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document.write( "Line AD has slope (12-5)/(7-3) = 7/4<BR>\n" );
document.write( "Line CB must has the same slope and must pass thru C(9,2)<BR>\n" );
document.write( "2 = (7/4)9 + b<BR>\n" );
document.write( "b = 8/4 -63/4 = -55/4<BR>\n" );
document.write( "CB has equation y = (7/4)x-55/4<BR>\n" );
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document.write( "B is at the intersection of AB and CB.<BR>\n" );
document.write( "(-1/2)x + (31/2) = (7/4)x-(55/4)<BR>\n" );
document.write( "(9/4)x = 117/4<BR>\n" );
document.write( "x = 13<BR>\n" );
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document.write( "Substitute into y = (-1/2)x+31/2 to solve for y:<BR>\n" );
document.write( "y = (-1/2)(13)+(31/2)<BR>\n" );
document.write( "y = -13/2 + 31/2<BR>\n" );
document.write( "y = 9<BR>\n" );
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document.write( "Coordinates of B need to be (13,9)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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