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3 and 4 .Determinants and Matrices
medium
Find area of the triangle with vertices at the point given in each of the following: $(-2,-3),(3,2),(-1,-8)$
A
$15$ square units
B
$12$ square units
C
$14$ square units
D
$20$ square units
Solution
The area of the triangle with vertices $(-2,-3),(3,2),(-1,-8)$ is given by the relation,
$\Delta=\frac{1}{2}\left|\begin{array}{ccc}-2 & -3 & 1 \\ 3 & 2 & 1 \\ -1 & -8 & 1\end{array}\right|$
$=\frac{1}{2}[-2(2+8)+3(3+1)+1(-24+2)]$
$=\frac{1}{2}[-2(10)+3(4)+1(-22)]$
$=\frac{1}{2}[-20+12-22]$
$=-\frac{30}{2}=-15$
Hence, the area of the triangle is $|-15|=15$ square units
Standard 12
Mathematics
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