Answer:
[tex]Area = 20[/tex]
Step-by-step explanation:
Given
[tex]\large A\left(-4,-2\right), \large B\left(1,3\right), \large C\left(4,-2\right).[/tex]
Required
The area
The area of a triangle is:
[tex]Area = \frac{1}{2}|A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y)|[/tex]
So, we have:
[tex]Area = \frac{1}{2}|-4(3 - -2) + 1(-2 - -2) + 4(-2 - 3)|[/tex]
[tex]Area = \frac{1}{2}|-4*5 + 1*0 + 4*-5|[/tex]
[tex]Area = \frac{1}{2}|-40|[/tex]
[tex]Area = \frac{1}{2}*40[/tex]
[tex]Area = 20[/tex]
