Question

Consider a triangle whose vertices are $(1,1),$ $(4,2)$ and $(3,5).$ Then the area this triangle is

• A. $3$ sq. units
• B. $7$ sq. units
• C. $5$ sq. units
• D. $10$ sq. units

Answer 1

The correct option is C $5$ sq. units

We know that the area of triangle whose vertices are $(x_1,y_1),$ $(x_2,y_2)$ and $(x_3,y_3)$ is given by
$\Delta =\left|\frac{1}{2}\left|\begin{array}{ccc}{x}_1& y_1& 1\\ x_2& y_2& 1\\ x_3& y_3& 1\end{array}\right|\right|$

$\Rightarrow \Delta =\left|\frac{1}{2}\left|\begin{array}{ccc}1& 1& 1\\ 4& 2& 1\\ 3& 5& 1\end{array}\right|\right|$

$\Rightarrow \Delta =\frac{1}{2}|1(2-5)-1(4-3)+1(20-6)|$
$\Rightarrow \Delta =\frac{1}{2}\times |(-3-1+14)|$
$\Rightarrow \Delta =5$ sq. units