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  4. If the vertices of a triangle are (-2,6)(3,-6) and (1,5), then the area of the triangle is

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Q. If the vertices of a triangle are $(-2,6)(3,-6)$ and $(1,5)$, then the area of the triangle is

KCETKCET 2022Determinants

Solution:

$\Delta=\frac{1}{2}\begin{vmatrix}-2-3 & -2-1 \\ 6+6 & 6-5\end{vmatrix}=\frac{1}{5}\begin{vmatrix}-5 & -3 \\ 12 & 1\end{vmatrix}$
$=\frac{1}{2}|-5+36|=\frac{31}{2}=15.5$