Question

HELP ASAP!!!!!!!!!!!!!!!!

Answer 1

The correct answer is: Option (A) $\frac{v-z}{w-x}$
 
Explanation:
If both lines are parallel, then their slopes must be equal.
 
For the line PQ, the slope is:
Slope of PQ = $\frac{v-z}{w-x}$ --- (1)
 
For the line P'Q', the slope is:
Slope of P'Q' = $\frac{v+b-z-b}{w+a-x-a}$ 
Slope of P'Q' = $\frac{v-z}{w-x}$ --- (2)
 
As (1) = (2), hence the lines are parallel and their slope is $\frac{v-z}{w-x}$ (Option A).

Answer 2

Answer:

Slope of both the lines are same.

Step-by-step explanation:

Line PQ contains points P(x,z) and Q(w,v)

similarly line P'Q' contains points P'(x+a, z+b) and Q'(w+a, v+b)

As we know slope of parallel lines are same, so to prove PQ and P'Q' we will show that these lines have same slope.

Slope of PQ = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{v-z}{w-x}$

Slope of P'Q' = $\frac{y_{2-y_{1} } }{x_{2}-x_{1}}$

= $\frac{(v+b)-(z+b)}{(w+a)-(x+a)}$

= $\frac{v+b-z-b}{w+a-x-a}=\frac{v-z}{w-x}$

So slope of both the lines are same, and both the lines have slope equivalent to $\frac{(v-z)}{(w-x)}$