Final answer:
The missing quantity in the slopes of Line PQ and Line P'Q' is the same, (w – x), which simplifies from the given (w + a) – (x + a), meaning both lines have slopes that are parallel to each other. Therefore, the correct answer is (b) (w – x) + (a – a); parallel.
Step-by-step explanation:
The given problem asks about the slopes of two lines, PQ and P'Q'. The slope of Line PQ is (v – z) divided by an unknown quantity, and the slope of Line P'Q' is divided by (w + a) – (x + a), which simplifies to (w – x) since the a terms cancel out. The statement suggests that both lines have the slope factor in common, indicating that they could be parallel. The missing denominator for Line PQ must be the same as that for Line P'Q', making the correct answer (w – x) given that:
slope of PQ = · (v – z) / · (w – x) and
slope of P'Q' = · (v – z) / · (w – x).
Hence, both lines are parallel, which brings us to the correct answer, which is (b) (w – x) + (a – a); parallel.