Login/Sign Up
Find the area of the triangle whose vertices are: $A(-8,-2), B(-4,-6)$ and $C(-1,5)$
Find the area of the triangle whose vertices are: $A(-8,-2), B(-4,-6)$ and $C(-1,5)$
CBSE | Class 12 | Determinants | Exercise 6C | Maths | RS Aggarwal
Find the area of the triangle whose vertices are: $A(-8,-2), B(-4,-6)$ and $C(-1,5)$

Solution:

Area of a triangle $=\frac{1}{2}\left|\begin{array}{lll}\mathrm{x}_{1} & \mathrm{y}_{1} & 1 \\ \mathrm{x}_{2} & \mathrm{y}_{2} & 1 \\ \mathrm{x}_{3} & \mathrm{y}_{3} & 1\end{array}\right|$
$=\frac{1}{2}\left|\begin{array}{ccc}
-8 & -2 & 1 \\
-4 & -6 & 1 \\
-1 & 5 & 1
\end{array}\right|$
Expanding with $R_{3}$
$\begin{array}{l}
=\frac{1}{2}[(-20-6)-(-40-2)+(48-8)] \\
=\frac{1}{2}[-26+42+40] \\
=\frac{56}{2} \\
=28 \text { sq. units }
\end{array}$

i

More Material