<p>R is the midpoint of line segment PT, and Q is the midpoint of line segment PR. If S is a point betwen R and t such that the length of segment QS is 10 and the length of segment PS is 19, what is the length of segment ST?</p>
<p>(A) 13
(B) 14
(C) 15
(D) 16
(E) 17</p>
<p>Please explain this problem to me! Thanks.</p>
<p>correct ans is (E)17,</p>
<p>P----Q----R-S-----------T</p>
<p>Given,
QS=10, PS=19</p>
<p>PS=QS+PQ -> 19=10+PQ -> PQ=9=QR (bcoz Q is midp of PR)
now, QS=QR+RS -> 10=9+RS -> RS=1
now, PR=RT=PQ+QR=9+9=18 (bcoz R is midp of PT so PR=PQ+QR=RT)
18=RT -> 18=RS+ST ->18=1+ST -> ST=17.(E)</p>
<p>The answer is 17. It helps if you draw it. </p>
<p>-p---q---r----s------t
-----q---10--s
-p----19-----s</p>
<p>Q to S is 10. P to S is 19. So that means PQ is 9 because Q is the midpoint of P-R. 19-10 = 9. </p>
<p>QR also equals 9 since Q is the midpoint of PR and PQ equals 9. </p>
<p>So PR is equal to 18. Therefore, RT is also equal to 18 because R is the midpoint of PT. </p>
<p>Since QS is equal to 10 and QR is equal to 9, you can deduce that RS is 1. </p>
<p>RT is 18 so subtract one from that and you get 17.</p>
<p>I hope my explnantion isn't confusing.</p>
<p>---9---9----18---
-p---q---r-------t</p>
<p>-1---17--
r--s-----t</p>
<p>Damn, porkey, beat me to it. At least I know I was right...</p>
<p>^ ya ur right lol</p>
<p>Thanks guys.</p>