Question

The area of triangle whose vertices are $A(-3,-1),B(5,3)$ and $C(2,-8)$ is ____ $\text{sq. units}$.

• A. $34\text{sq. units}$
• B. $36\text{sq. units}$
• C. $38\text{sq. units}$
• D. $32\text{sq. units}$

Answer 1

Answer: (C)

$38\text{sq. units}$

We know that the area of the triangle whose vertices are $(x_1,y_1),(x_2,y_2),$ and $(x_3,y_3)$ is $\frac{1}{2}\left|x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right|$

The given vertices of the triangle are $A(-3,-1),B(5,3)$ and $C(2,-8)$.

So, by using the above formula,

$\begin{array}{cc}\text{Area of the triangle}& =\frac{1}{2}[-3(3-(-8))+5(-8-(-1))+2(-1-3\left)\right]\\ & =\frac{1}{2}[-33-35-8]\\ & =\frac{[-76]}{2}\\ & =\frac{76}{2}\dots \left[\text{Area can never be negative so, we ignore negative sign}\right]\\ & =38\text{sq. units}\end{array}$

So, the area of the triangle is equal to $38\text{sq. units}$.