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

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

If the vertices of $\Delta LMN$ are $L(1,4), M(4,1)$ and $N(4,4),$ then $\Delta LMN$ is.......

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

If $P(1, 12)$ divides the line segment $\overline{AB}$ starting from $A$ in the ratio $2:1$ and $A(3, 8)$,then the coordinates of $B$ are $\ldots \ldots$

Prove that $(2a, 4a)$, $(2a, 6a)$, and $(2a + \sqrt{3}a, 5a)$ are the vertices of an equilateral triangle.