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

If the points $A(1, 2)$,$O(0, 0)$,and $C(a, b)$ are collinear,then:

Find the coordinates of the point which divides $\overline{AB}$ in the ratio $3:2$ from $A$. The coordinates of $A$ and $B$ are $(3, 2)$ and $(-2, -5)$ respectively.

If the midpoints of the sides $\overline{AB}$,$\overline{BC}$,and $\overline{CA}$ in $\Delta ABC$ are respectively $D(1, 2)$,$E(2, 1)$,and $F(3, 3)$,then find the centroid of $\Delta ABC$.

The distance of the point $P$ on the $X-$axis from $A(11, 12)$ is $13$ units. The coordinates of $P$ are $\ldots \ldots \ldots \ldots$.

Find the points on the $x$-axis which are at a distance of $2\sqrt{5}$ from the point $(7, -4)$. How many such points are there?