Question

S is between T and V. R is between S and T. T is between R and Q. QV=18, QT=6, and TR=RS=SV. Find RS , QS , TS , and TV.

Answer 1

                                             4                     4               4
-----Q-----------------------T----------------R---------------S---------------V
      <----------6----------->
      <-----------------------------------------18--------------------------------->


QT = 6 (given)
QV = 18 (given)
TR=RS=SV (given)

Then TV = 18-6 = 12 and since TR=RS=SV , then each segment = 12/3 =4

RS = 4
QS = 14
TS =  8
and TV. = 12

Answer 2

A line can have as many points as possible, and multiple lines can have similar points. The values of RS, QS, TS and TV are:

$RS = 4\\QS =14\\TV = 12\\TS = 8$  

S is a point between lines T and V means:

$TV = TS + SV$

R is a point between lines S and T means:

$TS = RS + TR$

T is a point between lines R and Q means

$RQ = TR + QT$

Given that:

$QT = 6\\QV = 18$

This means that Q is a point between lines QT and QV. So:

$TV = QV - QT$

$TV = 18- 6$

$TV = 12$

$TR=RS=SV$ means that:

$TV = TR+RS+SV$

Because $TR=RS=SV$, the equation becomes:

$TV = TR+TR+TR$

$TV = 3TR$

Substitute 12 for TV

$12 = 3TR$

Divide both sides by 3

$4 = TR$

$TR =4$

Hence:

$TR=RS=SV=4$

$TS = RS + TR$ gives

$TS = 4 + 4$

$TS = 8$

Next, we calculate the measure of QS from lines QV and SV

Point S is common between QS and SV. This means:

$QV = QS + SV$

Make QS the subject

$QS =QV -SV$

$QS =18-4$

$QS =14$

Hence, the values of RS, QS, TS and TV are:

$RS = 4\\QS =14\\TV = 12\\TS = 8$  

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