"R" is the midpoint of line segment "PT", nd "Q" is the midpoint of line segment "PR". If "S" is a point between "R" and "T" such that the length of segment "QS" is 10 and the length of segment "PS" is 19, what is the lenght of segment "ST"?
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Please provide the solution...
2006-11-03 09:56:05 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
P - - - - Q - - - - R - S - - - - - - - - T
PR = RT (midpoint)
PQ = QR (midpoint)
QS = 10, PS = 19
PQ = PS - QS
So PQ = 19 - 10 = 9
QR = 9
PR = PQ + QR = 18
RT = PR = 18
So the complete line PT = PR + RT = 18 + 18 = 36
ST = 36 - PS
ST = 36 - 19
ST = 17
2006-11-03 10:05:56 · answer #1 · answered by Puzzling 7 · 0⤊ 0⤋
Let segment sr=x and segment rs=y. Then x+y=10.
Since s is the midpoint of pr, segment ps + sr = 2x and ps =19 is the same as 2x+y=19. Now, to solve for x, subtract the first equation from the second equation to get:x=9. Since x=9, y=1. Because rt=pr=18 and rt=rs+st, st=17.
2006-11-03 10:05:47 · answer #2 · answered by bruinfan 7 · 0⤊ 1⤋
okay here is our line segment P Q R T
and S is somewhere inbetween R and T
QS = 10 and PS = 19
to find PQ we would take PS - QS = 19 - 10 = 9 = PQ
Then we know Q is the halfway point between P and R
So PR = 2*PQ = 2*9 = 18
And R is always between P and T
So PT = 2*PR = 2*18 = 36
So we have PT = 36 (total length) and PS = 19 (given)
ST = PT - PS = 36 - 19 = 17
2006-11-03 10:06:44 · answer #3 · answered by rachie_grl6 2 · 0⤊ 1⤋
First draw the problem. The ordering of the letters, from left to right should go: P, Q, R, S, T. R is right in the middle, Q half-way between P and R, and S is somewhere between R and T:
P────Q────R──S──────T
|<─x──>|<─x─>|<-y->|<─(2x-y)->|
________|<──10──>|
|<─────19─────>|
Now you can write some equations:
1) x + y = 10 ──► x = 10 - y
2) 2x + y = 19 ──► 2(10 - y) + y = 19
──► 20 - 2y + y = 19 ──► 20 - y = 19
──► y = 1
Substitute this intop equation (1):
x + 1 = 10 ──► x = 9
So the distance from S to T is:
2x - y = 2(9) - 1 = 17
2006-11-03 10:13:02 · answer #4 · answered by Anonymous · 1⤊ 1⤋
PS = 19,
QS = 10,
therefore, PQ = PS - QS
= 19 - 10
= 9
ie PQ = QR = 9
since Q is the midpoint of PR, PR = 2PQ
= 2(9)
= 18
and since R is the midpoint of PT, PR = RT = 18
QS = QR + RS
10 = 9 + RS
RS = 10 - 9
= 1
Therefore, to find ST:
RT = RS + ST
ST = RT - RS
= 18 - 1
= 17.
2006-11-03 10:39:07 · answer #5 · answered by genipabu 2 · 0⤊ 1⤋
PS-QS=PQ=9
so PT=9*4=36
ST=PT-PS=36-19=17
2006-11-03 10:11:26 · answer #6 · answered by raj 7 · 0⤊ 1⤋
P Q R S T
9 9 1 1
ST =1
2006-11-03 10:02:21 · answer #7 · answered by Chris 4 · 0⤊ 3⤋
19-10=PQ=9
PQ is 1/4 PT
PT=9x4=36
ST=PT-PS=36-19=17
2006-11-03 10:03:48 · answer #8 · answered by Anonymous · 0⤊ 1⤋
ST=17
I promise
2006-11-03 10:11:39 · answer #9 · answered by Luke D 2 · 0⤊ 1⤋