If the distance between $(3, a)$ and $(4, 1)$ is $\sqrt{10},$ then the value of $a$ is $ \ldots \ldots \ldots \ldots .$

$P$ is a point on $\overline{AB}$ such that $A - P - B$. $A(x_{1}, y_{1})$ and $B(x_{2}, y_{2})$ are the given points. If point $P$ divides $\overline{AB}$ from $A$ in the ratio $m : n$ (where $\frac{m}{n} > 0$),then the coordinates of $P$ are:

If three vertices of a parallelogram $ABCD$ are $A(1, 2)$,$B(2, 1)$,and $C(3, -4)$,then the coordinates of $D$ are.............

$P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$ are the given points. If $\overline{PQ}$ is parallel to the $X$-axis,then $PQ = \dots$

$P(0, 1/2)$,$Q(1/2, 1/2)$,and $R(1/2, 0)$ are respectively the midpoints of sides $\overline{AB}$,$\overline{BC}$,and $\overline{CA}$ in $\Delta ABC$. Find the coordinates of $A$,$B$,and $C$.

$P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$ are the given points. If $\overline{PQ}$ is parallel to the $Y$-axis,then $PQ = \dots$