If $A(0,0)$,$B(0,12)$,and $C(5,0)$,then $BC = \ldots$

Find the value of $m$ if the points $(5,1), (-2,-3)$ and $(8,2m)$ are collinear.

Find the ratio in which the point $P \left(\frac{3}{4}, \frac{5}{12}\right)$ divides the line segment joining the points $A \left(\frac{1}{2}, \frac{3}{2}\right)$ and $B(2, -5)$. (in $: 5$)

Find the area of a pentagon having the vertices $(1, 5), (-2, 4), (-3, -1), (2, -3),$ and $(5, 1).$

The distance between $A(2,4)$ and $B(-3,4)$ is............

$P$ 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: