Question

The vertices of a triangle are \large A\left(-4,-2\right), \large B\left(1,3\right) and \large C\left(4,-2\right).

Answer 1

`Area = 20`

Explanation:

Given

`\large A\left(-4,-2\right), \large B\left(1,3\right), \large C\left(4,-2\right).`

Required

The area

The area of a triangle is:

`Area = (1)/(2)|A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y)|`

So, we have:

`Area = (1)/(2)|-4(3 - -2) + 1(-2 - -2) + 4(-2 - 3)|`

`Area = (1)/(2)|-4*5 + 1*0 + 4*-5|`

`Area = (1)/(2)|-40|`

`Area = (1)/(2)*40`

`Area = 20`