Question

Determine the missing information in the paragraph proof.

Given: Line PQ contains points (w, v) and (x, z) and line P'Q' contains points (w + a, v + b) and (x + a, z + b). Lines PQ and P'Q' are parallel.

Prove: Parallel lines have the same slope.

On a coordinate plane, 2 lines are shown. Line Q P goes through (w, v) and (x, z). Line Q prime P prime goes through (w + a, v + b) and (x + a, z + b).

Since slope is calculated using the formula m = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction, 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.



StartFraction v minus z + b Over x minus z + a EndFraction
StartFraction w minus x + a Over v minus z + b EndFraction

Answer 1

The slope of PQ is m = (z − v)/(x − w). For P'Q',
m' = ((z + b) − (v + b))/((x + a) − (w + a)) = (z − v)/(x − w),
so both slopes are (z − v)/(x − w) (equivalently (v − z)/(w − x)).