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

To determine if the points are collinear, we can find the determinant of the matrix formed by the coordinates of the points:

| -3 -9 1 |
| -5 -11 1 |
| 0 -7 1 |

= (-3)(-11)(1) + (-9)(0)(1) + (-5)(-7)(1) - (1)(-11)(0) - (1)(0)(-5) - (1)(-7)(-3)

= 33 + 35 + 35 + 0 + 0 + 21

= 124

Since the determinant is non-zero (124), the points are not collinear.

Use a Determinant to Determine Whether the Points (-3,-9), (-5,-11)and