document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203060>Question 1203060</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The vertices of a square are (-2,2),(3,4),(5,-1) and(0,-3).Find the coordinates of the center of the square.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838310 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=838310\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Hint:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Label the four points as A,B,C,D\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A = (-2,2)<BR>\n" );
document.write( "B = (3,4)<BR>\n" );
document.write( "C = (5,-1)<BR>\n" );
document.write( "D = (0,-3)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is what the diagram looks like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=math_tutor2020&illustration_name=Screenshot_226.png\"><BR>\n" );
document.write( "I used GeoGebra to make the diagram. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The goal is to find the location of point E.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "One very useful property about squares is the diagonals bisect each other.<BR>\n" );
document.write( "Bisect means \"to cut in half\".<BR>\n" );
document.write( "Therefore, AE = EC and BE = ED.<BR>\n" );
document.write( "The diagonals intersect to form the center.<BR>\n" );
document.write( "This tells us that E is the midpoint of diagonal AC.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To go from A to C, we follow the pathway \"down 3, right 7\". Cut each of those values in half so we know how to go from A to E.<BR>\n" );
document.write( "I'll let the student do this part.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Other methods are possible. One alternative is to find the equations of lines AC and BD. <BR>\n" );
document.write( "Then use substitution or elimination to find the coordinates of point E.<BR>\n" );
document.write( "The first method I mentioned is a faster route in my opinion.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );