document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201240>Question 1201240</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 12,<BR>\n" );
document.write( "quations of two adjacent sides of a rhombus are: <BR>\n" );
document.write( "𝑦 = 2𝑥 + 4 and 𝑥 + 3𝑦 = 12,<BR>\n" );
document.write( "1.2.1 If (12, 0) is one vertex and all vertices have positive coordinates, find the <BR>\n" );
document.write( "coordinates of the other three vertices. Leave your answers in surd form </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835545 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) The second vertex is the intersection of the two lines forming a side of the rhombus.  Solve the pair of equations to find that second vertex is (0,4).  (I leave the details to you.)<br><BR>\n" );
document.write( "(2) Use the Pythagorean Theorem and the first two vertices to find the length of the side of the rhombus is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%2810%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "(3) A third vertex is on the line y = 2x + 4, a distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%2810%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the right and above (0,4).  Since the slope of that line is 2, this third vertex is x units to the right and 2x units above (0,4).  This gives us a right triangle with legs of length x and 2x and a hypotenuse of length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%2810%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Use that to find that x is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "Now you have enough to find the coordinates of the third and fourth vertices.<br><BR>\n" );
document.write( "I leave the details of the calculations to you.<br><BR>\n" );
document.write( "VERTICES:<BR>\n" );
document.write( "(12,0)<BR>\n" );
document.write( "(0,4)<BR>\n" );
document.write( "(4*sqrt(2),4+8*sqrt(2))<BR>\n" );
document.write( "(12+4*sqrt(2),8*sqrt(2))<br><BR>\n" );
document.write( "------------------------------------------------------------------<br><BR>\n" );
document.write( "Note that in fact the problem as stated is impossible: two of the vertices have a coordinate that is NOT positive. To solve the problem we have to ignore the instruction that says all coordinates of the vertices are positive.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );