Math 403: Homework 2


Book problems: 1.16, 1.18, 1.20, 1.22
and two extra problems about barycentric coordinates. In class, we learned that writing a point in barycentric coordinates
P=aA+bB+cC
is equivalent to writing
P-A=b(B-A)+c(C-A).
If the X coordinates of the vectors P-A, B-A, and C-A are X1, X2, and X3, respectively (and the Y coordinates are Y1, Y2, and Y3), then we have two equations
X1=bX2+cX3
and
Y1=bY2+cY3
in the two unknowns b and c to solve.

P1. Let A=(1,1), B=(2,3), and C=(4,2). Find the barycentric coordinates of P=(3,0) and Q=(0,3).

P2. Let A=(4,5), B=(5,5), and C=(6,7). Find the barycentric coordinates of P=(7,-3) and Q=(5,10).

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