The line x = c cuts the triangle with corners (0, 0), (1, 1) and (9, 1) into two regions. For the area of the two regions to be the same, c must be equal to_.

$\text{ Area of }\mathrm{\Delta }OAB=\frac{1}{2}\left(1\right)\left(8\right)=4\mathrm{sq}.\text{ units }$

$\text{ Equation of }OB\text{ is }y=\frac{1}{9}x\text{ . }$

$\text{ Hence point }E\text{ is }\left(c,\frac{c}{9}\right)\text{ . }$

$Area of the right angled triangle DEB is 2 sqaure units$

$\begin{array}{l}\Rightarrow \frac{1}{2}\left(1-\frac{c}{9}\right)(9-c)=2\\ \Rightarrow (9-c{)}^2=36\\ \Rightarrow 9-c=\pm 6\\ \Rightarrow c=3\end{array}$