Find area of triangle with vertices at point given in each of following: (-2,-3),(3,2),(-1,-8)

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3 and 4 .Determinants and Matrices

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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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