Prove parallel lines have the same slope. use lines r and s. line s is a vertical translation of line r.    (1)a translation is a rigid transformation. how does this statement support line s being parallel to line r?     (2)write an expression for the slope of line r.    (3)write an expression for the slope of line s.    (4)line q is a vertical translation of line s 3 units down. p" is the image of p'. what are the coordinates of p"? **for 1-4 you have to answer the question**

(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=

(3)

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

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

(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)

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm