If the midpoint of the line segment joining the points $(5, a)$ and $(b, 7)$ is $(3, 5)$,find $(a, b)$.

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:

The points of trisection of the line segment joining the points $(0, 3)$ and $(6, -3)$ are:

What is the distance between the points $(2, 15^{\circ})$ and $(1, 75^{\circ})$ in polar coordinates?

If the midpoint of the line segment joining the points $(5, a)$ and $(b, 7)$ is $(3, 5)$,then $(a, b) =$