Question

Triangle DEF, with vertices D(-8,-9), E(-3,-6), and F(-7,-4), is drawn on the coordinate grid below.

Answer 1

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,

`\begin{gathered} A=(1)/(2)|x_1\mleft(y_2-y_3\mright)+x_2(y_3-y_1)+x_3(y_1-y_2)| \\ =(1)/(2)|(-8)_{}(-6-(-4))+(-3)(-4-(-9))+(-7)(-9-(-6))| \\ =(1)/(2)|(-8)(-2)+(-3)(5)+(-7)(-3)| \\ =(1)/(2)|16-15+21| \\ =(1)/(2)|22| \\ =11\text{ square units.} \end{gathered}`

Hence, the area of the given triangle is 11 square units.