In each of these problems give  examples where the math concept is used in graphics

1. Give a parametric formula for a line segment between the points (1,2,3) and (3,5,7).
2. Give a parametric formula for the Bezier Curve determined by points (0,0), (1,0), (1,1), (2,2)
1. What are the tangents to the curve at (0,0) and (2,2)
3. In plane calculate the P matrix for rotating the i and j vectors by 45 degrees to get new vectors i' , j'
1. Show that coordinates in i',j' are the old coordinates in i,j rotated by -45 degrees.
4. Suppose a camera is pointed in the z direction with the y axis as up and the x axis pointing to right (z is pointing into screen as in computer graphics).
   
1. Where does the point (1,2,5) project to under an orthographic projection along z axis.
2. If you rotate the camera  by 45 degrees about the z axis  (x axis going towards y axis) where does the same point transform to in the new image.
5. What is the 4X4 matrix that scales uniformly by 3, then rotates 90 degrees counterclockwise (positively) around y axis , then translates by (1,2,3) and then does a perspective projection with a camera in standard position pointed along z axis with y up and x to right and the view plane at z=1.
6. Where does the line  through the origin and through the point (1,2,3) hit the plane x+y+z= 15. Is this point on the ray from the origin through (1,2,3) or in the opposite direction?
7. Consider the triangle in the plane (0,0), (2,2),(3,3). What is the convex combination of the vertices of this triangle that gives you the point (1,1).
8. Show that in the online bilinear interpolation calculator that the coefficients are convex. Show that  if
   you put in the coordinates for Q11-->(x1,y1), Q21-->(x2,y1)  you get the coordinates of P-->(x,y).