Suppose A, B, and C are vertices of a triangle in R2, and D is a point in R2. a. Use the

QUESTION:

Suppose A, B, and C are vertices of a triangle in R2, and D is a point in R2. a. Use the fact that the vectors AB and AC are linearly independent to prove that we can write D = rA + sB + tC for some scalars r, s, and t with r + s + t = 1. (Here, we are treating A, B, C, and D as vectors in R2.) b. Use Exercise 3 to show that t is the ratio of the signed area of _ABD to the signed area of _ABC (and similar results hold for r and s).