Question

determine the missing information in the paragraph proof. given: line pq contains points (w, v) and (x, z) and line pq contains points (w + a, v + b) and (x + a, z + b). lines pq and pq are parallel. prove: parallel lines have the same slope. since slope is calculated using the formula m = (y2 - y1)/(x2 - x1), the slope of both lines is equivalent to _______. it is given that the lines are parallel, and we calculated that the slopes are the same. therefore, parallel lines have the same slopes. options: (z - v)/(x - w), (x - w)/(z - v), (v - z + b)/(x - z + a), (w - x + a)/(v - z + b)

Explanation:

Step1: Calculate slope of line PQ

Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, for line PQ with points $(w,v)$ and $(x,z)$, the slope $m_{PQ}=\frac{z - v}{x - w}$.

Step2: Calculate slope of line P'Q'

For line P'Q' with points $(w + a,v + b)$ and $(x + a,z + b)$, the slope $m_{P'Q'}=\frac{(z + b)-(v + b)}{(x + a)-(w + a)}=\frac{z - v}{x - w}$.

Answer:

A. $\frac{z - v}{x - w}$