Find area of triangle with vertices at point given in each of following: (1,0),(6,0),(4,3)

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3 and 4 .Determinants and Matrices

easy

Find area of the triangle with vertices at the point given in each of the following: $(1,0),(6,0),(4,3)$

A

$\frac{11}{2}$ square units

B

$\frac{17}{2}$ square units

C

$\frac{15}{2}$ square units

D

$\frac{19}{2}$ square units

Solution

The area of the triangle with vertices $(1,0),(6,0),(4,3)$ is given by the relation,

$\Delta=\frac{1}{2}\left|\begin{array}{lll}1 & 0 & 1 \\ 6 & 0 & 1 \\ 4 & 3 & 1\end{array}\right|$

$=\frac{1}{2}[1(0-3)-0(6-4)+1(18-0)]$

$=\frac{1}{2}[-3+18]=\frac{15}{2}$ square units

Standard 12

Mathematics

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