QuestionAssessments / studyculx
Question 1 (a) The coordinates of three points are $A(2,-6), B(6,-12)$, and $C(-4,3)$. Find the perpendicular distance from $A$ to $\bar{B} C$. Based on your answer, what can you conclude about the relationship between the points $A, B$, and $C$ ?

Studdy Solution
Analyze the result to determine the relationship between points $A$, $B$, and $C$.
Since the perpendicular distance from $A$ to line $\overline{BC}$ is non-zero, point $A$ does not lie on the line $\overline{BC}$. Therefore, points $A$, $B$, and $C$ are not collinear.
The perpendicular distance from $A$ to $\overline{BC}$ is:
$$\boxed{\frac{12}{\sqrt{13}}}$$
Conclusion: Points $A$, $B$, and $C$ are not collinear.