Determinants are used to show that three points lie on the same line (are collinear). If
-Determinants are used to show that three points lie on the same line (are collinear). If $$\left| \begin{array} { l l l }
x _ { 1 } & y _ { 1 } & 1 \
x _ { 2 } & y _ { 2 } & 1 \
x _ { 3 } & y _ { 3 } & 1
\end{array} \right| = 0 ,$$
then the points $\left( \mathrm { x } _ { 1 } , \mathrm { y } _ { 1 } \right) , \left( \mathrm { x } _ { 2 } , \mathrm { y } _ { 2 } \right)$, and $\left( \mathrm { x } _ { 3 } , \mathrm { y } _ { 3 } \right)$ are collinear. If the determinant does not equal 0 , then the points are not collinear Are the points $( 10 - 9 ) , ( 0,5 )$ and $( 30 - 36 )$ collinear?
A)No
B)Yes

Question

Determinants are used to show that three points lie on the same line (are collinear). If
-Determinants are used to show that three points lie on the same line (are collinear). If $$\left| \begin{array} { l l l } 
x _ { 1 } & y _ { 1 } & 1 \
x _ { 2 } & y _ { 2 } & 1 \
x _ { 3 } & y _ { 3 } & 1
\end{array} \right| = 0 ,$$
then the points $\left( \mathrm { x } _ { 1 } , \mathrm { y } _ { 1 } \right) , \left( \mathrm { x } _ { 2 } , \mathrm { y } _ { 2 } \right)$, and $\left( \mathrm { x } _ { 3 } , \mathrm { y } _ { 3 } \right)$ are collinear. If the determinant does not equal 0 , then the points are not collinear Are the points $( 10 - 9 ) , ( 0,5 )$ and $( 30 - 36 )$ collinear?
A)No
B)Yes

Quizplus · Accepted Answer

The points are $(1,0.5), (0,5), (-6,0)$. We can check if they are collinear by computing the determinant: $$\left| \begin{array} { l l l } 
1 & 0.5 & 1 \
0 & 5 & 1 \
-6 & 0 & 1
\end{array} \right| = (-6)(0.5)(1)+(0)(1)(-6)+(5)(1)(-3)= -15\neq 0$$Since the determinant is not 0, the points are not collinear. Therefore, the answer is A)No.

Determinants Are Used to Show That Three Points Lie on the Same