Two points $(a, 0)$ and $(0, b)$ are joined by a straight line. Another point on this line is:

If $a, b$ and $c$ are in $AP$, then the straight line $ax + 2by + c = 0$ will always pass through a fixed point whose coordinates are

If the line passing through the points $(4, 3)$ and $(2, \lambda)$ is perpendicular to the line $y = 2x + 3$,then find the value of $\lambda$.

If a line intercepted between the coordinate axes is trisected at a point $A(4, 3)$,which is nearer to the $x$-axis,then its equation is

One diagonal of a square is along the line $8x - 15y = 0$ and one of its vertices is $(1, 2)$. Then the equations of the sides of the square passing through this vertex are:

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: