If the points $A(6, -1)$,$B(1, 3)$ and $C(x, 8)$ are such that $AB = BC$,then $x = $

The line $x + y = 4$ divides the line segment joining the points $(-1, 1)$ and $(5, 7)$ in the ratio:

What are the Cartesian coordinates of $(2, \pi /4)$?

The distance between the points $(7, 5)$ and $(3, 2)$ is equal to ........... $unit$.

Consider three points $P = (-\sin(\beta - \alpha), -\cos \beta)$,$Q = (\cos(\beta - \alpha), \sin \beta)$,and $R = (\cos(\beta - \alpha + \theta), \sin(\beta - \theta))$,where $0 < \alpha, \beta, \theta < \frac{\pi}{4}$. Then:

If $A$ and $B$ are the points $(-3, 4)$ and $(2, 1)$,then the coordinates of the point $C$ on $AB$ produced such that $AC = 2 BC$ are: