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

question 9

Multiple Choice

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) \(\mathrm { No }\)

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