State whether the following statement is true or false. Justify your answer.
Points $A(3, 1)$,$B(12, -2)$,and $C(0, 2)$ cannot be the vertices of a triangle.

(A) True.
Let the coordinates be $A(x_1, y_1) = (3, 1)$,$B(x_2, y_2) = (12, -2)$,and $C(x_3, y_3) = (0, 2)$.
The area of a triangle with vertices $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$ is given by the formula:
$\text{Area} = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$
Substituting the given values:
$\text{Area} = \frac{1}{2} |3(-2 - 2) + 12(2 - 1) + 0(1 - (-2))|$
$\text{Area} = \frac{1}{2} |3(-4) + 12(1) + 0(3)|$
$\text{Area} = \frac{1}{2} |-12 + 12 + 0|$
$\text{Area} = \frac{1}{2} |0| = 0$
Since the area of the triangle formed by these points is $0$,the points are collinear (they lie on the same straight line).
Therefore,these points cannot form a triangle. Thus,the statement is true.