Reading: Read the rest of BEG, chapter 2. There will be review problems given in class and on the web during the week.

1. (10 points) Given a triangle ABC, let P be a point inside the triangle. Let line AP intersect line BC at A'. Use facts about areas of triangles to show (a), (b), (c).

   (a) Show that the ratio BA'/A'C = area(ABA')/area(AA'C).

   (b) Show that the ratio BA'/A'C = area(ABP)/area(APC).

   (c) State Ceva's Theorem and show how this follows from (a) and (b) applied to the three triangles areas ABP, BCP, and CAP, without using the other proofs of Ceva that you have seen.

   (d) Show in an example what happens to this picture when P lies outside the triangle. Are the same ratio equalities true? Which ratios and which areas become negative?

2. (5 points) BEG p 93, 2.4 # 3
3. (5 points) BEG p 93, 2.4 # 5
4. (5 points) BEG p 93, 2.4 # 6
5. (5 points) BEG p 93, 2.5 # 1
6. (5 points) BEG p 93, 2.5 # 2
7. (10 points) Bezier conics (see handout)

   (a) Find the parametric equation of the Bezier conic whose control polygon has vertices (-1, 1) (0, -1), (1,1).

   (b) Find the equation in x and y for this curve and point out that this is a parabola.

   (c) Explain why any two Bezier conics are affine congruent.