Question

If vertices of triangle are $(2,4),(5,k),(3,10)$ and its area is $15squareunit$, find value of $k$

Answer 1

$\begin{array}{c}\left(2,4\right),\left(5,k\right),\left(3,10\right)\\ \Rightarrow Areaofrectangle=\frac{1}{2}\left[2\left(k-10\right)+5\left(10-4\right)+3\left(4-k\right)\right]\\ \Rightarrow 2\times 15=\left(2k-20+30+12-3k\right)\\ \Rightarrow 30=22-k\\ \therefore k=-8\end{array}$