In $\Delta ABC$,if $A(1, 7)$,$B(2, 4)$,and $C(k, 5)$ and $\angle A$ is a right angle,then find the value of $k$.

In $\Delta ABC$,$A(1, 2)$,$B(3, 4)$,and $C$ lies on the $X$-axis. If the centroid $G$ of $\Delta ABC$ is on the $Y$-axis,then find the coordinates of $C$.

$P$ 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:

The distance between the points $(0, 5)$ and $(-5, 0)$ is

If $P(at^{2}, 2at)$,$Q(\frac{a}{t^{2}}, \frac{-2a}{t})$ and $S(a, 0)$ are three points,show that $\frac{1}{SP} + \frac{1}{SQ}$ is independent of $t$.

$A$ point $(4,4)$ divides the line segment joining $A(2,6)$ and $B(6,2)$ from $A$,then the ratio of division is $\ldots \ldots \ldots \ldots .$