The points 1 + 3i,5 + i,and 3 + 2i in the com | vedclass

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(B) Let $z_1 = 1 + 3i$,$z_2 = 5 + i$,and $z_3 = 3 + 2i$. These points correspond to the coordinates $(1, 3)$,$(5, 1)$,and $(3, 2)$ in the Cartesian pl

Vedclass · Accepted Answer

Collinear

Vedclass · Answer

(B) Let $z_1 = 1 + 3i$,$z_2 = 5 + i$,and $z_3 = 3 + 2i$. These points correspond to the coordinates $(1, 3)$,$(5, 1)$,and $(3, 2)$ in the Cartesian plane. The area of the triangle formed by these points is given by: $A = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$ $A = \frac{1}{2} |1(1 - 2) + 5(2 - 3) + 3(3 - 1)|$ $A = \frac{1}{2} |1(-1) + 5(-1) + 3(2)|$ $A = \frac{1}{2} |-1 - 5 + 6| = \frac{1}{2} |0| = 0$. Since the area is $0$,the points are collinear.

The points $1 + 3i$,$5 + i$,and $3 + 2i$ in the complex plane are

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