document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148059>Question 148059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1)	The points A(1,6), B(6,6), C(4,3), D(-1,3) are vertices of a quadrilateral.  Prove that the quadrilateral is a parallelogram.  (Show that line AB ll line DC and line AD ll BC)<BR>\n" );
document.write( "2)	The points T(-1,4), E(2,4), and D(2,-1) are vertices of a triangle.  Prove that the triangle is a right triangle.  (Find the slopes of line TE, line ED and line TD.)<BR>\n" );
document.write( "3)	The points L(3,1), O(2,-3), V(-2,-2) and E(-1,2) are vertices of a rhombus.  Show that the diagonal are perpendicular.<BR>\n" );
document.write( "4)	Solve y = mx + b for x.  Use the result to find x in y = 4x – 5 when y = 3. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108445 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=108445\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll show you how to do question 1. Questions 2 and 3 are use the same technique - so you can solve them. \r<BR>\n" );
document.write( "\n" );
document.write( "1) (The points A(1,6), B(6,6), C(4,3), D(-1,3) are vertices of a quadrilateral.  Prove that the quadrilateral is a parallelogram.\r<BR>\n" );
document.write( "\n" );
document.write( "You need to remember that parallel lines have the same slope and perpendicular lines have slopes that are negative reciprocal (the product of the slopes of two perpendicular lines equals -1.\r<BR>\n" );
document.write( "\n" );
document.write( "So find the slopes is the segments AB and CD. Then find the slopes of segments BC and DA.\r<BR>\n" );
document.write( "\n" );
document.write( "slope when given two points. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Slope of AB is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bab%5D=++%286-6%29%2F%286-1%29 ALIGN=MIDDLE  ALT=\"m%5Bab%5D=++%286-6%29%2F%286-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Slope of CD is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bcd%5D=++%283-3%29%2F%28-1-4%29 ALIGN=MIDDLE  ALT=\"m%5Bcd%5D=++%283-3%29%2F%28-1-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Both are 0, so they are parallel\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Slope of BC is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bbc%5D=++%283-6%29%2F%284-6%29 ALIGN=MIDDLE  ALT=\"m%5Bbc%5D=++%283-6%29%2F%284-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Slope of DA is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bcd%5D=++%283-1%29%2F%28-1-1%29 ALIGN=MIDDLE  ALT=\"m%5Bcd%5D=++%283-1%29%2F%28-1-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Both are -2/3, so they are parallel too. \r<BR>\n" );
document.write( "\n" );
document.write( "A figure with two sets of parallel lines is a a prallelogram\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2) For problem two, find the slopes of the three segments. Then verify that two of those slopes have a product of -1. \r<BR>\n" );
document.write( "\n" );
document.write( "3)For problem three, find the slopes of the segments LV and OE. The show they have a product of -1\r<BR>\n" );
document.write( "\n" );
document.write( "4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+mx+%2B+b ALIGN=MIDDLE  ALT=\"y+=+mx+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+b+=+mx ALIGN=MIDDLE  ALT=\"y+-+b+=+mx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-b%29%2Fm+=+x+ ALIGN=MIDDLE  ALT=\"%28y-b%29%2Fm+=+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Solve when y = 3, m=4 and b = -5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283+-+%28-5%29%29%2F4+=+x ALIGN=MIDDLE  ALT=\"%283+-+%28-5%29%29%2F4+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F4+=+x ALIGN=MIDDLE  ALT=\"8%2F4+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+=+x ALIGN=MIDDLE  ALT=\"+2+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );