Question

Find the area of the triangle whose vertices are

$(2,3)(-1,0),(2,-4)$

Answer 1

We have,

$(x_1,y_1)=(2,3)$

$(x,y_2)=(-1,0)$

$(x_3,y_3)=(2,-4)$

We know that,

Area of triangle

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

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

$=\frac{1}{2}\left|[8+7+6]\right|$

$=\frac{1}{2}\left|21\right|$

$=\frac{21}{2}\text{sq}\text{.}\text{unit}$