Chapter 2: Project

Part I

A 6 by 12 special pool table is determined by the y-axis, x-axis, the vertical line x = 6, and the horizontal line y = 12 (see depiction below). The pool table obeys the special pool rule: “When a ball bounces off one of the sides of the table, its slope post-bounce is the opposite of its slope pre-bounce”.

(a)    What are the coordinates of the six pockets A, B, C, D, E, and F?

(b)   Calculate the distance between the pockets A and D.

(c)    What are the coordinates of the center G of the table?

(d)   What are the exact coordinates of the points where the diagonals AD and CF meet the circle centered at G and of radius 2?

(e)    Suppose your pool ball is at (3,8). You hit it towards the y-axis along the line with slope 2. Where does it hit the y-axis? Where does it hit the side of the table next? and after that? and after that? Would it return to the point (3,8)? Assume the ball was hit hard enough.

Part II (extra)

The tangent line to a circle is defined as a line that meets the circle at a single point. Such a point is referred to as the point of tangency (see depiction below).

Suppose the circle is centered at the origin and is or radius r > 0. Suppose further that the line has slope m and y-intercept b.

Verify that:

(a)    The  

(Hint. The binomial  is a complete square.)

(b)   The point of tangency has coordinates .

(c)    The tangent line is perpendicular to the line passing through the origin and the point of tangency.