The area of the triangle with vertices  (2,7), (1,1), (10,8) is

# The area of the triangle with vertices  $\left(2,7\right),\text{\hspace{0.17em}}\left(1,1\right),\text{\hspace{0.17em}}\left(10,8\right)$ is

1. A

16 sq. units

2. B

$\frac{37}{2}$ sq. units

3. C

$\frac{47}{2}$ sq. units

4. D

$\frac{50}{3}$ sq. units

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### Solution:

The area of the triangle with the vertices  $\left(2,7\right),\text{\hspace{0.17em}}\left(1,1\right),\text{\hspace{0.17em}}\left(10,8\right)$ is

$\Delta =\frac{1}{2}\left|\begin{array}{ccc}2& 7& 1\\ 1& 1& 1\\ 10& 8& 1\end{array}\right|=\frac{1}{2}\left[-16+63\right]$

$=\frac{47}{2}$ sq. units.

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