Question

Prove parallel lines have the same slope. Use lines f and g. Line g is a vertical translation of line f.

Please help

Answer 1

(1)

since a translation of a line segment is its rigid movement, vertically or horizontally.

line 's' is parallel to line 'r' since it is a translation of line 'r' 'e' units vertically ( clearly we could see that the point P' corresponding to point P in line r is shifted 'e' units upward and point Q' in line 's' is formed by shifting corresponding point Q of line 'r' e units upward).

(2)

the slope of a line is defined as the change in y-coordinates to the change in x-coordinates of the points on that line.

slope of line r=slope of line segment PQ.

coordinates of P=(m,n) and Q=(j,k)

slope of line r=slope of PQ=
k-n ÷ j-m

(3)

the slope of line s= slope of line segment P'Q'

slope of line s=slope of P'Q'=
k+e- (n+e) ÷ j-m
=

k-n ÷ j-m

(4)

as line q is a vertical translation of line 's' 3 units down.

and P'' is the image of P'.

so coodinates of P''= (m,n+e-3)

Answer 2

The slope of both lines is 1/4.

Explanation:

Line g is a vertical translation of line f so they are parallel. Now find the slope of each line.

Line f joins points (-2, 1) and (2, 2), so its slope is (2 - 1) / [2 - (-2)] = 1/4.

Line g joins points (-2, -1) and (2, 0), so its slope is [0 - (-1)] / [2 - (-2)] = 1/4.

The two parallel lines have the same slope.