Chapter 7.8, Problem 3E

To determine

To state the number required to multiply and find the area of the triangle.

Answer to Problem 3E

The area of the triangle is obtained by multiplying the value of determinant by $\frac{1}{2}$ .

Explanation of Solution

Given information :

The given three points, $\left(x_1,y_1\right)\left(x_2,y_2\right)\left(x_3,y_3\right)$ are the vertices of the triangle.

The value of the determinant is given as $-6$ .

The area of a triangle with vertices $\left(x_1,y_1\right)\left(x_2,y_2\right)\left(x_3,y_3\right)$ is,

Area $=\pm \frac{1}{2}\left|\begin{array}{ccc}{x}_1& y_1& 1\\ x_2& y_2& 1\\ x_3& y_3& 1\end{array}\right|$

Here the symbol $\pm$ indicates that the appropriate sign should be chosen to yield a positive area.

Since, the value of the determinant is given as $-6$ , the area of the triangle can be obtained by multiplying it by $\frac{1}{2}$ to yield a positive area.

Therefore,

The area of the triangle is obtained by multiplying the value of determinant by $\frac{1}{2}$ .