geometry help.?

Question

a coordinate grid is marked on apool table. a pool ball is positioned at point (1,6) and must roll and strike the midpoint of the segment on the cushion with endpoints(2,0) and (8,0). Find the slope of the incoming path of the ball and the slope of the outgoing path of the ball.

please explain. im confused.

Answer 1

Given starting point P(1,6).
The midpoint of (2,0) and (8,0) is M(5,0).

The slope of the line thru (2,0) and (8,0) is zero.

Incoming slope m.

m = slope from P to M.
m = ∆y/∆x = (0 - 6)(5 - 1) = -6/4 = -3/2

Outgoing path of ball. The angle of reflection equals the angle of incidence. Since the ball is bouncing off a horizontal line the outgoing slope m' is as below.

m' = -m = 3/2

Answer 2

The midpoint is (5,0)
The normal (line vertical to the endpoints) is x=5

Map the point (1,6) across the line x=5
Its image will be at (9,6)

Slope of incoming path of the ball:
(0-6)/(5-1) = -1.5

Slope of outgoing path of the ball will be:
(6-0)/(9-5) = 1.5