document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185154>Question 1185154</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.The points A(-7, -7), B(8, -1), C(4, 9), D are the vertices of the parallel ogram ABCD. Find the coordinates of D. Prove that ABCD is a rectangle and find its area.\r<BR>\n" );
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document.write( "b.  Find the equation of the line which is parallel to the line 3x + 4y = 12 and which makes an intercept of 5 units on the x-axis. Find also the equation of the line which is perpendicular to the given line and which passes through the point (4, 5). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #815925 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=815925\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sketch this and the three points are in quadrants III, IV, and I. So the other point is in quadrant 2.<BR>\n" );
document.write( "The slope between A and B is change in y/change in x=6/15 or 2/5.<BR>\n" );
document.write( "the slope between B and C is 10/-4 or -5/2, which is the negative reciprocal of 2/5, so the lines are perpendicular. ANSWER<BR>\n" );
document.write( "Now look at distances. A and B, the long side, distance is sqrt (15^2+6^2)=sqrt(261).<BR>\n" );
document.write( "Need the same distance from C to D. <BR>\n" );
document.write( "Call D (x, y)<BR>\n" );
document.write( "Then sqrt(( x-4)^2+(9-y)^2)=sqrt(261).<BR>\n" );
document.write( "the x distance has to be 15, so it is x=-11.<BR>\n" );
document.write( "The y distance has to be 6, so it is y=3. Only that way will the distance be sqrt(261) Again, check the sketch.<BR>\n" );
document.write( "D is (-11, 3); A is (-7, -7) ANSWER<BR>\n" );
document.write( "Prove this is a rectangle by looking at the slope between A and D. It should be -5/2. It is =-10/4, so that is OK.<BR>\n" );
document.write( "Now look at the distance between A and D, and that is sqrt (16+100)=sqrt (116).<BR>\n" );
document.write( "Compare with the parallel lie BC, which has distance sqrt(16+100)=sqrt (116)<BR>\n" );
document.write( "The lines are parallel to each other, perpendicular to each other, and opposite sides are of equal length. That is a rectangle.<BR>\n" );
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document.write( "The area, in square units, is sqrt(261)*sqrt(116)=174 square units. ANSWER<BR>\n" );
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document.write( "3x+4y=12<BR>\n" );
document.write( "4y=-3x+12<BR>\n" );
document.write( "y=-(3/4)x+3<BR>\n" );
document.write( "parallel line has slope of -3/4 and point at (5, 0)<BR>\n" );
document.write( "point slope formula, y-y1=m(x-x1), m slope (x1, y1) a point,<BR>\n" );
document.write( "y=-(3/4)(x-5)<BR>\n" );
document.write( "y=-(3/4)x+(15/4) ANSWER<BR>\n" );
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document.write( "perpendicular line to the given line has slope of (4/3) and goes through (4, 5)<BR>\n" );
document.write( "y-5=(4/3)(x-4)<BR>\n" );
document.write( "y=(4/3)x-(1/3)<BR>\n" );
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document.write( " </SPAN>\n" );
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