Question

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

Answer 1

Slope of both the lines are same.

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 =
`(y_(2)-y_(1))/(x_(2)-x_(1))=(v-z)/(w-x)`

Slope of P'Q' =
`\frac{y_{2-y_(1) } }{x_(2)-x_(1)}`

=
`((v+b)-(z+b))/((w+a)-(x+a))`

=
`(v+b-z-b)/(w+a-x-a)=(v-z)/(w-x)`

So slope of both the lines are same, and both the lines have slope equivalent to
`((v-z))/((w-x))`

Answer 2

The correct answer is: Option (A)
`(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 =
`(v-z)/(w-x)` --- (1)

For the line P'Q', the slope is:
Slope of P'Q' =
`(v+b-z-b)/(w+a-x-a)`
Slope of P'Q' =
`(v-z)/(w-x)` --- (2)

As (1) = (2), hence the lines are parallel and their slope is
`(v-z)/(w-x)` (Option A).