The Area of a Triangle with Vertices $\left( x _ { 1 } , y _ { 1 } \right),$

question 21

Multiple Choice

The area of a triangle with vertices $\left( x _ { 1 } , y _ { 1 } \right) ,$ $\left( x _ { 2 } , y _ { 2 } \right) ,$ and $\left( x _ { 3 } , y _ { 3 } \right)$ can be given as the absolute value of the determinant $\frac { 1 } { 2 } \left| \begin{array} { l l l } x _ { 1 } & y _ { 1 } & 1 \\x _ { 2 } & y _ { 2 } & 1 \\x _ { 3 } & y _ { 3 } & 1\end{array} \right|$ Use this formula to find the area of each triangle whose coordinates are $( - 6,2 ) ,$ $( 0,3 ) ,$ and $( - 5,6 ) .$

• A)11.0
• B)1.0
• C)15.5
• D)11.5
• E)6.0

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