Use the formula $$\text { Area } = \pm \frac { 1 } { 2 } \left| \begin{array} { l l l }
x _ { 1 } & y _ { 1 } & 1 \
x _ { 2 } & y _ { 2 } & 1 \
x _ { 3 } & y _ { 3 } & 1
\end{array} \right|$$ to find the area of the triangle with the given vertices. Choose the
+ or - sign so that the value of the area is positive.
-$$( 5,4 ) , ( - 5,1 ) , ( - 2 , - 2 )$$
A) 39
B) $\frac { 39 } { 2 }$
C) $- \frac { 39 } { 2 }$
D) $- 39$

Question

Use the formula $$\text { Area } = \pm \frac { 1 } { 2 } \left| \begin{array} { l l l } 
x _ { 1 } & y _ { 1 } & 1 \
x _ { 2 } & y _ { 2 } & 1 \
x _ { 3 } & y _ { 3 } & 1
\end{array} \right|$$ to find the area of the triangle with the given vertices. Choose the
+ or - sign so that the value of the area is positive.
-$$( 5,4 ) , ( - 5,1 ) , ( - 2 , - 2 )$$
A) 39
B) $\frac { 39 } { 2 }$
C) $- \frac { 39 } { 2 }$
D) $- 39$

Quizplus · Accepted Answer

The formula for the area of a triangle given its vertices $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ is $\frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$. Substituting the given points into this formula yields an area of $\frac{39}{2}$.

Use the Formula To Find the Area of the Triangle with the Given