The line $x + y = 4$ divides the line segment joining the points $(-1, 1)$ and $(5, 7)$ in the ratio:

The distance between the points $(7, 5)$ and $(3, 2)$ is equal to ........... $unit$.

In what ratio does the $x$-axis divide the line segment joining the points $(3, -4)$ and $(-5, 6)$?

In what ratio does the line $3x + 4y = 7$ divide the line segment joining the points $(1, 2)$ and $(-2, 1)$?

$P$ and $Q$ are points on the line joining $A,(-2, 5)$ and $B,(3, 1)$ such that $AP = PQ = QB$. Then the mid-point of $PQ$ is

The point $A$ divides the join of the points $(-5, 1)$ and $(3, 5)$ in the ratio $k : 1$. The coordinates of the points $B$ and $C$ are $(1, 5)$ and $(7, -2)$ respectively. If the area of the triangle $ABC$ is $2$ square units,then $k =$