Question

Cara is playing pool. She wants to use the cue ball C to hit the ball at point A without hitting the ball at point B. To do so, she has to bounce the cue ball off the side rail and into the ball at point A. Find the coordinates of the exact point along the side rail that Cara should aim for.

Answer 1

This might take a little imagination, but you need to imagine that the cue travels in a straight line with a total y displacement of (4-1)=3 units and a total x displacement of (4+2)=6 units.

Now you can find the slope of this line...dy/dx=3/6=1/2

Now that we know the slope is 1/2 we simply apply it to the cue position...

y=x/2+b, using the cue position (1,1) to solve for b

1=1/2+b, b=1/2 thus our line is:

y=(x+1)/2

Now the cue ball must travel four units along the x-axis until it meets the rail so:

y=(4+1)/2=2.5

So the point that you need to aim at is (5, 2.5)

Answer 2

Three point four or four point three