What is the distance between the points $(a, 0)$ and $(0, a)$?

The distance of the midpoint of the line segment joining the points $(a \sin \theta, 0)$ and $(0, a \cos \theta)$ from the origin is:

If the line joining the points $A(b \cos \alpha, b \sin \alpha)$ and $B(a \cos \beta, a \sin \beta)$ is extended to the point $N(x, y)$ such that $AN: NB = b: a$,then

What are the coordinates of the points of trisection of the line segment joining the points $(-3, -3)$ and $(6, 6)$?

Let $A = (a_1, a_2)$ and $B = (b_1, b_2)$ be two points in the plane with integer coordinates. Which one of the following is not a possible value of the distance between $A$ and $B$?

If the coordinates of two opposite vertices of a square are $(a, b)$ and $(b, a)$,find the area of the square.