Answer
Points are not collinear.
Work Step by Step
To calculate the slope between points $(x_1,y_1)$ and $(x_2,y_2)$, we use the formula:
$slope=m=\frac{y_2-y_1}{x_2-x_1}$
We calculate the slope between the points $A(0,6)$ and $B(4,-5)$:
$slope=\frac{-5-6}{4-0}=\frac{-11}{4}=-\frac{11}{4}$
Next, we calculate the slope between the points $B(4,-5)$ and $C(-2,12)$:
$slope=\displaystyle \frac{12-(-5)}{-2-4}=\frac{17}{-6}=-\frac{17}{6}$
Since the two slopes are not the same, we know that the three points can not be collinear (we do not need to calculate the slope of AC).
