I just need to do this quick. Summary,
7^2+b^2=12^2

C) coordinates of P' (1, - 3).

Step-by-step explanation:

Given  : The point P(6, –1) is translated according to the rule (x, y) → (x – 5, y – 2).

To find : What are the coordinates of P'.

Solution : we have given point P(6, –1) .

By the  rule (x, y) → (x – 5, y – 2).

Where x = 6 ,y = -1.

After translation point become :

Then P(6, –1)  →P' (6 – 5, -1 – 2).

P(6, –1)  →P' (1, - 3).

Therefore, C) coordinates of P' (1, - 3).