Use a determinant and the given vertices of a triangle to find the area of the triangle.
(-2, 5), (3, 3), (-1, 6)

A) $\frac { 7 } { 2 }$
B) $\frac { 2 } { 19 }$
C) $\frac { 3 } { 7 }$
D) $\frac { 6 } { 11 }$
E) $\frac { 5 } { 17 }$

Question

Use a determinant and the given vertices of a triangle to find the area of the triangle.  
(-2, 5), (3, 3), (-1, 6)
 
A) $\frac { 7 } { 2 }$
B) $\frac { 2 } { 19 }$
C) $\frac { 3 } { 7 }$
D) $\frac { 6 } { 11 }$
E) $\frac { 5 } { 17 }$

Quizplus · Accepted Answer

The area of a triangle given vertices $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ can be found using the determinant formula: $\frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$. Plugging in the given points (-2, 5), (3, 3), and (-1, 6) into this formula gives $\frac{1}{2} |-2(3 - 6) + 3(6 - 5) - 1(5 - 3)| = \frac{1}{2} |6 + 3 - 2| = \frac{7}{2}$.

Use a Determinant and the Given Vertices of a Triangle 72\frac { 7 } { 2 }27​

Use a Determinant and the Given Vertices of a Triangle $\frac { 7 } { 2 }$