Question

8) findthe area of triangle
a) (2, 3) (-1,0) and (2, -4)
b) (-5, -1) (3,-5) and (5,2).... ​

Answer 1

Answer:

    a) 10.5

    b) 32

Step-by-step explanation:

Key fact:

• The area of the triangle with vertices at (a,b), (c,d) and (e,f) is given by the determinant:

                               $\displaystyle\frac12\left|\begin{matrix}1&1&1\\a&c&e\\b&d&f\end{matrix}\right|$

a) Area =

$\displaystyle\tfrac12\left|\begin{matrix}1&1&1\\2&-1&2\\3&0&-4\end{matrix}\right|\\\\=\tfrac12\left(-\left|\begin{matrix}2&2\\3&-4\end{matrix}\right|-\left|\begin{matrix}1&1\\3&-4\end{matrix}\right|\right)\\\\=\tfrac12(8+6+4+3)=\tfrac12\times21=10.5$

(b) Area =

$\displaystyle\tfrac12\left|\begin{matrix}1&1&1\\-5&3&5\\-1&-5&2\end{matrix}\right|\\\\=\tfrac12\left(\left|\begin{matrix}3&5\\-5&2\end{matrix}\right|-\left|\begin{matrix}-5&5\\-1&2\end{matrix}\right|+\left|\begin{matrix}-5&3\\-1&-5\end{matrix}\right|\right)\\\\=\tfrac12(6+25+10-5+25+3)=\tfrac12\times64=32$