Given:
The three vertices of a triangle are D(-8,-9), E(-3,-6), and F(-7,-4).
To find its area:
Using the formula,
[tex]\begin{gathered} A=\frac{1}{2}|x_1\mleft(y_2-y_3\mright)+x_2(y_3-y_1)+x_3(y_1-y_2)| \\ =\frac{1}{2}|(-8)_{}(-6-(-4))+(-3)(-4-(-9))+(-7)(-9-(-6))| \\ =\frac{1}{2}|(-8)(-2)+(-3)(5)+(-7)(-3)| \\ =\frac{1}{2}|16-15+21| \\ =\frac{1}{2}|22| \\ =11\text{ square units.} \end{gathered}[/tex]
Hence, the area of the given triangle is 11 square units.
