document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090481>Question 1090481</A>: <I><SPAN STYLE=\"word-break: break-all;\"> P, Q, R, S and T are on line k such that Q is the midpoint of PT, R is the midpoint of QT, and S is the midpoint of RT. If PS = 9, then ehat is PT? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704927 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=704927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "Step 1) Draw out a horizontal line and label it k.<BR>\n" );
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document.write( "Step 2) Plot the points P, Q, R, S, T (in that order from left to right) on the line k<BR>\n" );
document.write( "This is what you should have so far<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/xuVvfqM.png\"><BR>\n" );
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document.write( "Step 3) <BR>\n" );
document.write( "Since \"S is the midpoint of RT\", we know that RS = ST = x which is marked in purple for the figure below. <BR>\n" );
document.write( "Since \"R is the midpoint of QT\", we know that QR = RT = y which is marked in green for the figure below. <BR>\n" );
document.write( "Since \"Q is the midpoint of PT\", we know that PQ = QT = z which is marked in red for the figure below. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/Eax8TxS.png\"><BR>\n" );
document.write( "x, y and z are unknown for now<BR>\n" );
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document.write( "Step 4)<BR>\n" );
document.write( "Note how two copies of x can be combined to form y. On one hand, RS+ST = RT and at the same time x+x = 2x = y (in step 3 we have RS = ST = x; RT = y). This means y = 2x. <BR>\n" );
document.write( "Put another way:<BR>\n" );
document.write( "RT = RS + ST<BR>\n" );
document.write( "RT = x + x<BR>\n" );
document.write( "RT = 2x<BR>\n" );
document.write( "RT = y<BR>\n" );
document.write( "So y = 2x<BR>\n" );
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document.write( "Step 5) <BR>\n" );
document.write( "Using similar logic used in step 4, we can say that z = 2y. This is because z = QT and QT = QR+RT = y+y = 2y. By the transitive property, if z = QT and QT = 2y, then z = 2y.<BR>\n" );
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document.write( "Step 6) <BR>\n" );
document.write( "Refer to the figure in step 3 to determine that<BR>\n" );
document.write( "PQ = z<BR>\n" );
document.write( "QR = y<BR>\n" );
document.write( "RS = x<BR>\n" );
document.write( "Note how PQ+QR+RS = PS by the segment addition postulate. <BR>\n" );
document.write( "So,<BR>\n" );
document.write( "PS = PQ+QR+RS<BR>\n" );
document.write( "PS = z+y+x<BR>\n" );
document.write( "PS = 2y+y+x ... z has been replaced with 2y (see step 5)<BR>\n" );
document.write( "PS = 2(2x)+2x+x ... every y has been replaced with 2x (see step 4)<BR>\n" );
document.write( "PS = 4x+2x+x<BR>\n" );
document.write( "PS = 7x<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Step 7) <BR>\n" );
document.write( "Back in the previous step, we found out that PS = 7x. We are given that PS = 9. Use the substitution property to say<BR>\n" );
document.write( "PS = 9<BR>\n" );
document.write( "7x = 9<BR>\n" );
document.write( "7x/7 = 9/7<BR>\n" );
document.write( "x = 9/7<BR>\n" );
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document.write( "Step 8) <BR>\n" );
document.write( "Now we can find the length of PT<BR>\n" );
document.write( "PT = PQ + QT<BR>\n" );
document.write( "PT = z + z<BR>\n" );
document.write( "PT = 2*z<BR>\n" );
document.write( "PT = 2*(2y) ... z has been replaced with 2y (see step 5)<BR>\n" );
document.write( "PT = 4*y<BR>\n" );
document.write( "PT = 4*(2x) ... y has been replaced with 2x (see step 4)<BR>\n" );
document.write( "PT = 8*x<BR>\n" );
document.write( "PT = 8*(9/7) ... x has been replaced wth 9/7 (see step 7)<BR>\n" );
document.write( "PT = 72/7<BR>\n" );
document.write( "PT = 10.2857142857142<BR>\n" );
document.write( "The decimal value is approximate. You can use long division or a calculator to come up with that result.<BR>\n" );
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document.write( "Answer as a fraction: <font color=red>72/7</font><BR>\n" );
document.write( "Answer in decimal form: <font color=red>10.2857142857142</font> (round this however you need to)<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );