The co-ordinates of the point which is equidistant from the three vertices of $△AOB$ (shown in the adjoining figure) are

The point on the $x-$axis which is equidistant from the points $A\left(-2, 3\right)$ and $B\left(5, 4\right)$ is

The ratio in which the $x-$axis divides the line segment joining the points $A\left(3, 6\right)$ and $B\left(9, -3\right)$ is

The perpendicular bisector of the line segment joining the points $A(1, 5)$ and $B(4, 6)$ cut the $y-$axis at

The area $\left(in square units\right)$ of the triangle formed by the points $A\left(5, 2\right), B\left(4, 7\right)$ and $C\left(7, -4\right)$ is