If the three points are $A(2, 3)$,$B(3, 1)$,and $C(5, 3)$,then the slope of the line passing through $A$ and bisecting $BC$ is:

Let the coordinates of the two points $A$ and $B$ be $(1, 2)$ and $(7, 5)$ respectively. The line $AB$ is rotated through $45^{\circ}$ in the anti-clockwise direction about the point of trisection of $AB$ which is nearer to $B$. The equation of the line in the new position is:

The area of the triangle formed by the line $L$ with the coordinate axes is $12$ sq. units. If $L$ passes through the point $(12, 4)$ and the product $P$ of the $X$-intercept of $L$ and the square of the $Y$-intercept of $L$ is negative,then $P=$

The equation of the line passing through the points $(1, 2)$ and $(2, 5)$ is:

If the portion of a line intercepted between the coordinate axes is divided by the point $(2, -1)$ in the ratio $3:2$,then the equation of that line is:

Find the equation of the line passing through the point $(1, -2)$ and making equal intercepts on the axes.