Consider a 2D triangle defined by the points a = (2, 2), b = (7, 1) and c = (3, 3), given in counterclockwise order. Solve the following and show your work. 1. Verify that point p = (3, 2) lies within the triangle by showing it lies to the "left" of each of the three oriented lines a b, b c, and c a. 2. Derive the expression for the three barycentric coordinates , , for any point p = (x, y) in the plane. Test three special points [(, ) = (0, 0), (0, 1), (1, 0)] to make sure your solution is correct. 3. What are the (x,y) coordinates of the point having barycentric coordinates (, ) = ( 1 3 , 1 3 )? 4. Verify that point p = (3, 2) lies within the triangle by computing its barycentric coordinates. What range of values of barycentric coordinates determines whether p lies within the triangle