Use a determinant to determine whether the points (-3, -9), (-5, -11) and (0, -7) are collinear.
A) $\left| \begin{array} { c c c }
- 3 & - 9 & 1 \
- 5 & - 11 & 1 \
0 & - 7 & 1
\end{array} \right| = 2 \text {; therefore, the points are not collinear }$
B) $\left| \begin{array} { c c c }
- 3 & - 9 & 1 \
- 5 & - 11 & 1 \
0 & - 7 & 1
\end{array} \right| = 0 \text {; therefore, the points are collinear }$

Question

Use a determinant to determine whether the points (-3, -9), (-5, -11) and (0, -7) are collinear.  
A) $\left| \begin{array} { c c c } 
- 3 & - 9 & 1 \
- 5 & - 11 & 1 \
0 & - 7 & 1
\end{array} \right| = 2 \text {; therefore, the points are not collinear }$
B) $\left| \begin{array} { c c c } 
- 3 & - 9 & 1 \
- 5 & - 11 & 1 \
0 & - 7 & 1
\end{array} \right| = 0 \text {; therefore, the points are collinear }$

Quizplus · Accepted Answer

The determinant of the matrix formed by the coordinates of the points and a column of ones is non-zero (2), indicating that the area of the triangle formed by the points is non-zero, and thus, the points are not collinear.

Use a Determinant to Determine Whether the Points (-3, -9)