Answer to Question #100411 in Geometry for Tarynn Wiese

Question

Draw triangle xyz with vertices x(-3,2),Y(4,-2), and z(-3,-2) on the coordinate plane.Then find the area of the triangle in square units

Answer 1

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

Plugging values,

$x_1=-3,x_2=4,x_3=-3$

$y_1=2,y_2=-2,y_3=-2$

Plugging the values in above formula,

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

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

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

$Area=\frac{1}{2}|0-16-12|$

$Area=\frac{1}{2}|-28|$

$Area=\frac{1}{2} \times{28}$

$Area=14$

So, area = 14 square units.