Evaluate a Third-Order Determinant
-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 $\left( x _ { 1 } , y _ { 1 } \right) , \left( x _ { 2 } , y _ { 2 } \right)$, and $\left( x _ { 3 } , y _ { 3 } \right)$ are collinear. If the determinant does not equal 0 , then the points are not collinear. Are the points $( 4 , - 4 ) , ( 0,3 )$, and $( 20 , - 32 )$ collinear?
A) Yes
B) $\mathrm { No }$

Question

Evaluate a Third-Order Determinant
-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 $\left( x _ { 1 } , y _ { 1 } \right) , \left( x _ { 2 } , y _ { 2 } \right)$, and $\left( x _ { 3 } , y _ { 3 } \right)$ are collinear. If the determinant does not equal 0 , then the points are not collinear. Are the points $( 4 , - 4 ) , ( 0,3 )$, and $( 20 , - 32 )$ collinear?
A) Yes
B) $\mathrm { No }$

Quizplus · Accepted Answer

The determinant equals 0, indicating that the points are collinear.

Evaluate a Third-Order Determinant -Determinants Are Used to Show That ∣x1y11x2y21x3y31∣=0,\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 ,​x1​x2​x3​​y1​y2​y3​​111​​=0,

Evaluate a Third-Order Determinant
-Determinants Are Used to Show That $\left| \begin{array} { l l l } x _ { 1 } & y _ { 1 } & 1 \\x _ { 2 } & y _ { 2 } & 1 \\x _ { 3 } & y _ { 3 } & 1\end{array} \right| = 0 ,$