Final answer:
To find the length of PR, solve for the midpoint Q and then add the lengths of PQ and QR.
Step-by-step explanation:
To find the length of PR, we need to find the length of PQ and QR first, and then add them together. Given that PQ = 2x + 9 and QR = -6x + 39, we can find the midpoint Q by equating the two expressions:
2x + 9 = -6x + 39
Solving for x, we get x = 6. Substituting this value back into the expressions for PQ and QR, we have PQ = 21 and QR = 3. Therefore, PR = PQ + QR = 21 + 3 = 24.
So, the length of PR is 24. Answer choice (a) 6x + 24 is correct.