Login/Sign Up
Find the area of the triangle whose vertices are: $A(-2,4), B(2,-6)$ and $C(5,4)$
Find the area of the triangle whose vertices are: $A(-2,4), B(2,-6)$ and $C(5,4)$
CBSE | Class 12 | Determinants | Exercise 6C
Find the area of the triangle whose vertices are: $A(-2,4), B(2,-6)$ and $C(5,4)$

Solution:

Area of a triangle $=\frac{1}{2}\left|\begin{array}{lll}\mathrm{x}_{1} & \mathrm{y}_{1} & 1 \\ \mathrm{x}_{2} & \mathrm{y}_{2} & 1 \\ \mathrm{x}_{3} & \mathrm{y}_{3} & 1\end{array}\right|$
$=\frac{1}{2}\left|\begin{array}{ccc}-2 & 4 & 1 \\ 2 & -6 & 1 \\ 5 & 4 & 1\end{array}\right|$
Expanding with $C_{3}$
$\begin{array}{l}
=\frac{1}{2}[(8+30)-(-8-20)+(12-8)] \\
=\frac{1}{2}[38+28+4] \\
=\frac{68}{2} \\
=34 \text { sq. units }
\end{array}$

i

More Material