Answer
Find out the Area of a triangle .
To proof
Formula
Area of Triangle
[tex]= \frac{1}{2}\times( {x_1(y_{2}-y_{3}) +x_{2}(y_{3} - y_{1})+x_{3}(y_{1}-y_{2})})[/tex]
Now vertices are D(3, 3) , E(3, −1) , and F(−2, −5) .
[tex]= \frac{1}{2} (3\times(-1 +5) + 3\times(-5-3)-2\times(3+1))[/tex]
Solving the above
[tex]= \frac{1}{2}(3\times4+3\times-8 -2\times4)[/tex]
[tex]=\frac{1}{2} (12-24-8)\\ =\frac{1}{2} (-32+12)\\=\frac{1}{2} (-20)[/tex]
= -10 units²
(Neglected the negative sign as area cannot be negative.)
= 10 units ²
Area of a triangle is 10 units ²
Hence proved
