Question

The value of $t$ if the area of the pentagon $ABCDE$ be $\frac{45}{2}$ where
$A=(1,3),B=(-2,5),C=(-3,-1),D(0,-2)$ and $E=(2,t)$ are

• A. $-1$
• B. $1$
• C. $2$
• D. $-2$

Answer 1

The correct option is A $-1$

Area of ABCDE $=\frac{1}{2}\left|\begin{array}{cc}1& 3\\ -2& 5\\ -3& -1\\ 0& -2\\ 2& t\\ 1& 3\end{array}\right|=\frac{45}{2}=>44-t=45=>t=-1$