Linear Algebra, 2020a

362 Chapter Four. Determinants
(b) [Petersen] Prove that the area of a triangle with vertices (x 1 ,y 1 ), (x 2 ,y 2 ), and
(x 3 ,y 3 ) is
1
x 1 x 2 x 3
2
y 1 y 2 y 3
∣ 1 1 1 ∣ .
(c) [Math. Mag., Jan. 1973] Prove that the area of a triangle with vertices at
(x 1 ,y 1 ), (x 2 ,y 2 ), and (x 3 ,y 3 ) whose coordinates are integers has an area of N or
N/2 for some positive integer N.