EXPLANATION:
Given;
We are given the triangle DEF on the coordinate plane. The coordinates are also given as follows;
[tex]F=(0,0),D=(8,0),E=(0,-2)[/tex]Required;
We are required to calculate the area of triangle DEF.
Step-by-step solution;
We shall begin by drawing up the triangle with the coordinates given, on a graph page;
Observe that the points DEF has been appropriately labeled. The length of side FD is 8 units (that is, from point 0 to 8), the length of side FE is 2 units.
We now have the base (side FE) and the vertical height (side FD), we can calculate the area of the triangle using the formula;
[tex]\begin{gathered} Area\text{ }of\text{ }a\text{ }triangle: \\ \\ Area=\frac{1}{2}bh \end{gathered}[/tex]Where the variables are;
[tex]\begin{gathered} base=2 \\ height=8 \end{gathered}[/tex]The area therefore is;
[tex]\begin{gathered} Area=\frac{1}{2}\times2\times8 \\ \\ Area=8 \end{gathered}[/tex]We now have;
ANSWER:
Area = 8 square units
The first option is the correct answer
