Answer:
Area = 18 square units
Step-by-step explanation:
Given
[tex]A =(2,-1)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]B =(5,6)[/tex] --- [tex](x_2,y_2)[/tex]
[tex]C = (-1,4)[/tex] --- [tex](x_3,y_3)[/tex]
Required
The area of the triangle
This is calculated as:
[tex]Area = \frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) +x_3(y_1 - y_2)|[/tex]
[tex]Area = \frac{1}{2} * |2(6 - 4) + 5(4 - -1) -1(-1 -6)|[/tex]
[tex]Area = \frac{1}{2} * |2*2 + 5*5 -1*-7|[/tex]
[tex]Area = \frac{1}{2} * |36|[/tex]
[tex]Area = \frac{1}{2} * 36[/tex]
Area = 18 square units
