8. (a) Let R be a set of n red points and let B be a set of n blue points. All in the plane. Suggest an expected O(n)-time algorithm to determine if there is a line such that every blue point is above l, and every red point is below l. Hint: Write the line las y = ax + b. What are the constrains on a and b that the points imposes? (b) Given R and B as above, find whether there is a line that separates them. (c) Repeat, but now R and B are points in Rd. You are allowed to use the Simplex Algorithm. Comments: in higher dimension, one could use the simplex method to find a separating hyper-plane. This methods sometimes referred to as the support vector machine. In other places, one adds more restrictions on the separating hyperplane (e.g. stay far away from all points)