The distance between the points $A(-3, 4)$ and $O(0, 0)$ is $OA = \dots$

Show that the point $(5, 5)$ is the midpoint of the line segment joining $(3, 5)$ and $(7, 5)$.

When point $A(x_{1}, y_{1})$ and point $B(x_{2}, y_{2})$ are joined to form $\overline{AB}$ and a point divides $\overline{AB}$ in the ratio $\lambda : 1$,the coordinates of the point are:

The coordinates of the point which is equidistant from the three vertices of the $\triangle AOB$ as shown in the figure are

State whether the following statement is true or false. Justify your answer.
Points $A(-6, 10)$,$B(-4, 6)$,and $C(3, -8)$ are collinear such that $AB = \frac{2}{9} AC$.

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 $t$.