The triangle with the vertices $(1, 1)$, $(-1, -1)$, and $(-\sqrt{3}, \sqrt{3})$ is $\ldots \ldots \ldots$ triangle.

The points $A(x_{1}, y_{1})$,$B(x_{2}, y_{2})$ and $C(x_{3}, y_{3})$ are the vertices of $\triangle ABC$.
$(i)$ The median from $A$ meets $BC$ at $D$. Find the coordinates of the point $D$.
$(ii)$ Find the coordinates of the point $P$ on $AD$ such that $AP : PD = 2 : 1$.
$(iii)$ Find the coordinates of points $Q$ and $R$ on medians $BE$ and $CF$,respectively,such that $BQ : QE = 2 : 1$ and $CR : RF = 2 : 1$.
$(iv)$ What are the coordinates of the centroid of the triangle $ABC$?

If $A (4, 7)$ and $B (7, 3),$ then $AB = .............$

Find the distance between the points $A(5, 8)$ and $B(1, 2)$.

If the mid-point of the line segment joining the points $A (3, 4)$ and $B (k, 6)$ is $P (x, y)$ and $x+y-10=0,$ find the value of $k.$

The line segment joining $A(-3, 5)$ and $B(2, 5)$ intersects............