document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172342>Question 1172342</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many squares on the co-ordinate plane exist with one vertex at P(-1,1) and having atleast one of the coordinate axes as axis of symmetry...?? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #797380 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=797380\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: 5\r<BR>\n" );
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document.write( "This diagram shows all the possible squares.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/VeOHxwP.png\"><BR>\n" );
document.write( "The five possbile squares are<BR>\n" );
document.write( "Square PABC (blue)<BR>\n" );
document.write( "Square PCDE (blue)<BR>\n" );
document.write( "Square PEFG (blue)<BR>\n" );
document.write( "Square PHCJ (red) <BR>\n" );
document.write( "Square PJEK (red) \r<BR>\n" );
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document.write( "The blue squares are all have side lengths of 2 units. The red squares have side lengths of sqrt(2) units. \r<BR>\n" );
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document.write( "Note how P is 1 unit above the x axis. Reflecting it over the x axis leads to point C. We can see that segment PC is 2 units long. So that explains why square PABC is 2 by 2, and only one such square is possible where P(-1,1) is in the upper right corner and the sides are vertical. Similar logic applies to the other 2 blue squares. \r<BR>\n" );
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document.write( "For the red squares, note how the axis of symmetry lies along the diagonals. If you reflect point E over the y axis, you arrive at point E. Points P and E are sufficient to form square PJEK, where P and E are opposite vertices. So only one red square is possible in this configuration. The other red square PHCJ is a similar story.<BR>\n" );
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