Math 445 Quiz 1

Problem 1

(a)    In the triangle below, AD = b, AE = c, BD = 1 and CE = 1. Find the barycentric coordinates of F.

(b)   If the area of triangle ABC = 10, what is the area of triangle FBC?

Problem 2

Let A = (1, 2, 3) and B = (81, 42, -29). 

(a)    Find the point C on line AB for which AC/CB = 5/3.

(b)   Find the point D on line AB for which AD/DB = -5/3.

(c)    Find the point E where line AB intersects the (x, y, 0) plane (i.e., the coordinate plane containing the x and y axes).

Problem 3

Suppose that point D has barycentric coordinates (2, 1, -2) with respect to triangle ABC. 

• If T is an affine transformation with T(A) = (1,1), T(B) = (-1,3), T(C) = (5,4), what point is T(D)? (The answer should be numerical, with no letters.)