Reflection Vector Research

Reflection Vector Research:

Vect1 is the direction of the ball before hitting the wall
Vect2 is after the wall
WallN is the normal of the wall
DOT is the dot product
Vect2 = Vect1 - 2 * WallN * (WallN DOT Vect1)
note that this will work for 3D vectors too

v' = 2 * (v . n) * n - v;
Where '*' is the scalar multiplication operator, '.' is the dot product of two vectors, and '-' is the subtraction operator for two vectors. v is reflected off of the surface, and gives a reflection vector v' which is used as the new velocity of the object.

Dot Product By Hand:
http://www.slideshare.net/ChelseaDarling0/trigonometry-lesson-dot-product

Trigonometry Lesson: Dot Product

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Basically: [1]Multiply the X components together.
           [2]Multiply the Y components together.
           [3]Add the X and Y of the new point2 value 
           together to get a single scalar float value.