document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=337062>Question 337062</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Points P, Q, and R lie in a plane. If the distance between P and Q is 5 and the distance between Q and R is 2, which of the following could be the distance between P and R ?<BR>\n" );
document.write( "I. 3 <BR>\n" );
document.write( "II. 5 <BR>\n" );
document.write( "III. 7<BR>\n" );
document.write( "(A) I only <BR>\n" );
document.write( "(B) II only <BR>\n" );
document.write( "(C) III only <BR>\n" );
document.write( "(D) I and III only <BR>\n" );
document.write( "(E) I, II, and III<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #241678 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=241678\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Points P, Q, and R lie in a plane. If the distance between P and Q is 5 and the distance between Q and R is 2, which of the following could be the distance between P and R ?<BR>\n" );
document.write( "I. 3 <BR>\n" );
document.write( "II. 5 <BR>\n" );
document.write( "III. 7<BR>\n" );
document.write( "(A) I only <BR>\n" );
document.write( "(B) II only <BR>\n" );
document.write( "(C) III only <BR>\n" );
document.write( "(D) I and III only <BR>\n" );
document.write( "(E) I, II, and III\r<BR>\n" );
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document.write( "distance PQ is the length of line PQ, distance QR is the length of line QR<BR>\n" );
document.write( "distance PR is the length of line PR and is unknown<BR>\n" );
document.write( "line PQ has length 5, line QR has length 2, line PR has length ?\r<BR>\n" );
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document.write( "these 3 lines form a triangle<BR>\n" );
document.write( "PR has to be between the difference of PQ and QR AND the sum of PQ and QR, due to the Triangle Inequality Theorem (part of the properties of triangles)<BR>\n" );
document.write( "PQ - QR = 5 - 2 = 3<BR>\n" );
document.write( "PQ + QR = 5 + 2 = 7\r<BR>\n" );
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document.write( "3 < PR < 7<BR>\n" );
document.write( "PR can not be 3 and PR can not be 7, UNLESS points are collinear (in a straight line)\r<BR>\n" );
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document.write( "(B) II only is answer, well if the 3 points are not collinear (in a straight line)\r<BR>\n" );
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document.write( "so answer is (E) I, II, and III\r<BR>\n" );
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document.write( "BUT case I and case III can only occur if the points are collinear\r<BR>\n" );
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