Question

Find the area of $\Delta$ PQR whose vertices are P (2,1), Q (3, 4) and R (5, 2).

Answer 1

Given $\Delta PQRP(2,1),Q(3,4),R(5,2)$

Area of $\Delta$ with vertices $(x_1,y_2)(x_2,y_2),(x_3,y_3)$

$\Delta =\frac{1}{2}\left|\begin{array}{ccc}{x}_1& y_1& 1\\ x_2& y_2& 1\\ x_3& y_3& 1\end{array}\right|$

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

$=\frac{1}{2}\left|\begin{array}{ccc}2& 1& 1\\ 1& 3& 0\\ 3& 1& 0\end{array}\right|$

$R_2\to R_2-R_1$

$R_3\to R_3-R_1$

$=\frac{1}{2}|1[9-1]|$

$=\frac{8}{2}=4$ sq. units