Question

The area of the triangle whose vertices are $(-2,-3),(3,2),$ and $(-1,-8)$ is:

• A. $5$ square units.
• B. $10$ square units.
• C. $15$ square units.
• D. $12$ square units.

Answer 1

The correct option is C $15$ square units.

The area of triangle with given vertices can be obtained as:

$k=\frac{1}{2}\left|\begin{array}{ccc}-2& -3& 1\\ 3& 2& 1\\ -1& -8& 1\end{array}\right|$

$\Rightarrow k=\left(1/2\right)[-2(2+8)+3(3+1)+1(-24+2\left)\right]$
$\Rightarrow k=\left(1/2\right)[-2(10)+3(4)+1(-22\left)\right]\Rightarrow k=\left(1/2\right)[-20+12-22]$
$\Rightarrow k=\left(1/2\right)[-42+12]$
$\Rightarrow k=\left(1/2\right)(-30)=-15$
So, the required area is $15$ square units.