Question

Find the area of region bounded by the triangle whose vertices are $(-2,1),(0,4)$ and $(2,3)$

Answer 1

We have,

$A(x_1,y_1)=(-2,1)$

$B(x_2,y_2)=(0,4)$

$C(x_3,y_3)=(2,3)$

We know that,

Area of triangle

$=|\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]|$

$=|\frac{1}{2}[-2(4-3)+0(3-1)+2(1-4)]|$

$=|\frac{1}{2}[-2\times 1+0-6]|$

$=|\frac{1}{2}(-8)|$

$=|-4|=4$

Hence, this is the answer.