Determinants and Matrices — Maths STD 11 Science — Question

$\begin{aligned} & B\left(x_2, y_2\right)=B(2,4) \\ & C\left(x_3, y_3\right)=C(0,0)\end{aligned}$

Area of a triangle $=\frac{1}{2}\left|\begin{array}{lll}x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1\end{array}\right|$

$\mathrm{A}(\Delta \mathrm{ABC})=\frac{1}{2}\left|\begin{array}{ccc}-1 & 2 & 1 \\ 2 & 4 & 1 \\ 0 & 0 & 1\end{array}\right|$

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

$=\frac{1}{2}(-4-4)=\frac{1}{2}(-8)=-4$

Since area cannot be negative, A(ΔABC) = 4 sq.units