Final answer:
The length of QQ' is found by subtracting QT from Q'T, resulting in QQ' = Q'T - QT = (6x - 16) - (3x - 4) which simplifies to 3x - 12. Hence, the correct answer is option C, 3x - 12.
Step-by-step explanation:
To find the length of QQ', we can evaluate the expressions given for QT and Q'T. Assuming that these line segments are on the same line and that Q' lies between Q and T, the length of QQ' can be found by subtracting the length of QT from Q'T.
We have QT = 3x – 4 and Q'T = 6x – 16. So, QQ' = Q'T – QT, which simplifies to:
(6x – 16) – (3x – 4)
After subtracting, we combine like terms:
(6x – 3x) + (–16 + 4)
This results in 3x – 12.
Therefore, the length of QQ' is 3x – 12, which corresponds to option C.