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3 and 4 .Determinants and Matrices
medium
નીચે આપેલાં શિરોબિંદુવાળા ત્રિકોણનું ક્ષેત્રફળ શોધો : $(2,7),(1,1),(10,8)$
A
$\frac{43}{2}$ square units
B
$\frac{45}{2}$ square units
C
$\frac{49}{2}$ square units
D
$\frac{47}{2}$ square units
Solution
The area of the triangle with vertices $(2,7),(1,1),(10,8)$ is given by the relation,
$\Delta=\frac{1}{2}\left|\begin{array}{ccc}2 & 7 & 1 \\ 1 & 1 & 1 \\ 10 & 8 & 1\end{array}\right|$
$=\frac{1}{2}[2(1-8)-7(1-10)+1(8-10)]$
$=\frac{1}{2}[2(-7)-7(-9)+1(-2)]$
$=\frac{1}{2}[-14+63-2]=\frac{1}{2}[-16+63]$
$=\frac{47}{2}$ square units
Standard 12
Mathematics
