math 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!

Answer 1

First, you need to calculate the midpoint of the cushion. The simplest way to do this is to take the mean average of the two x-coordinates and the mean average of the two y-coordinates.

((2 + 8)/2, (0 + 0)/2)
= (5,0)

Now you need to calculate the gradient of the straight line joining (1,6) and (5, 0). This is calculated by the change in y divided by the change in x

(0 - 6)/(5 - 1)
= -6/4
= -3/2

Slope: -3/2

The ball will rebound on a line with slope 3/2 (i.e. a mirror image)

Answer 2

This is just my guess.
Draw a grid, then draw the ball at (1,6) and the line from (2,0) to (8,0).
Then draw a line from the ball to the middle of the line which will be (5,0) - ("...must roll and strike the midpoint of the segment")

After that work out the gradient (change in y divided by change in x). Google "working out gradients" for help.

I dunno about the outgoing path part.

Hope this helps!

Answer 3

The target is (5,0).

Thus the slope of the incoming path is (0-6)/(5-1) = -3/2

The outgoing path will be a reflection of this: 3/2