Answer:
(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= [tex]\dfrac{k-n}{j-m}[/tex]
(3)
the slope of line s= slope of line segment P'Q'
slope of line s=slope of P'Q'= [tex]\dfrac{k+e-(n+e)}{j-m}=\dfrac{k-n}{j-m}[/tex]
(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)
