Problem 1: Suppose T is a Euclidean transformation T(x) = Ax + b. Find A and b if T(0,0) = G0, T(1,0) = G1, and T(0,1) = G2. In this case G0 = (2,3) and the segment G0G1 makes a 45-degree angle with the horizontal.

Problem 2. In the figure below is the major axis of an ellipse and its two foci.

1. Construct the points on the ellipse that lie on the line m through F1 which is perpendicular to A1A2
2. Construct the circle you would use in the "circle construction" of the ellipse with GSP.

Problem 3. In the triangle ABC below, two of the sides are divided into equal parts and parallel segments have been constructed. Let P be located at a point of intersection as show.

1. If line BP intersects AC at P2, what is the ratio AP2/P2C?
2. What are the barycentric coordinates of P? Or in other words, write P = aA + bB + cC. Tell what are the numbers a, b, c.