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Transpose of a Matrix

The value of ...

Question

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

A

- 1

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B

1

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C

2

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D

- 2

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Solution

The correct option is A $- 1$
Area of ABCDE $= \frac{1}{2} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 3 - 2 & 5 - 3 & - 1 0 & - 2 2 & t 1 & 3 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ = \frac{45}{2} => 44 - t = 45 => t = - 1$

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