More on Reflections

When a ball is rolled without spin against a wall, it bounces off the wall, as if it had gone through the wall and its path were reflected over the wall. In the picture below, a miniature golf ball A is hit against a wall. It bounces off the wall at point O and goes as the arrow shows.

In basketball, the same rules apply. In the picture below, ball A is bounce-passed to a teammate at location C. Again, angle AOB is equal to angle COD.

You can observe this exact situation in action in this video(240K Quicktime).

Sample Problem

If given a ball location A, a desired final location B, and a wall/floor to bounce off line l, there's a simple way to find where exactly the ball has to bounce off the wall in order to get to the desired location. Please refer to the picture below as you follow the directions.

First, reflect A over l. r l(A)=(C). Then, draw a line from C to A. The point where that line meets l (point E) is the point where the ball has to bounce off the wall. There, you have it!

Great, let me try a problem myself!

Since free throws became too easy for most players, the league decided to have some fun. For a free throw to count, you have to hit it off the ceiling! In case you make it to the NBA later, get some practice today! In the picture above, you see the net, the ball, the ceiling, and the reflection of the net over the ceiling. Just click the part of the ceiling where you think the ball has to bounce off in order to make it into the net.
Disclaimer: it was obviously a joke, the league is not planning to change the rules regarding free throws (although it would be fun to watch!)

Stumped? Take a look at the answer key!

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