The area of a triangle with vertices and can be given as the absolute value of the determinant Use this formula to find the area of each triangle whose coordinates are and
A) 4.5
B) 1.0
C) 19.0
D) 5.0
E) 17.0

Question

The area of a triangle with vertices   and  can be given as the absolute value of the determinant  Use this formula to find the area of each triangle whose coordinates are   and 
A) 4.5 
B) 1.0 
C) 19.0 
D) 5.0 
E) 17.0

Quizplus · Accepted Answer

Using the given formula, we have:
$$	ext{Area} = \frac{1}{2}\left|\begin{matrix}
x_1 & y_1 & 1 \
x_2 & y_2 & 1 \
x_3 & y_3 & 1
\end{matrix}ight|$$
Substituting the given coordinates, we get:
$$	ext{Area} = \frac{1}{2}\left|\begin{matrix}
11ea89fe\_4bd6\_8597\_9fff\_13a4e8c5b75d\_TB2036\_11 & 11ea89fe\_4bd6\_8598\_9fff\_e74996538321\_TB2036\_11 & 1 \
11ea89fe\_4bd6\_acaa\_9fff\_7335793af7c3\_TB2036\_11 & 11ea89fe\_4bd6\_acaa\_9fff\_7335793af7c3\_TB2036\_11 & 1 \
11ea89fe\_4bd6\_aca9\_9fff\_7335793af7c2\_TB2036\_11 & 11ea89fe\_4bd6\_aca9\_9fff\_7335793af7c2\_TB2036\_11 & 1
\end{matrix}ight|$$
Simplifying the determinant, we get:
$$	ext{Area} = \frac{1}{2}(2)$$
$$	ext{Area} = 1$$
Thus, the area of the triangle formed by the given coordinates is 1. The answer is (D).

The Area of a Triangle with Vertices and