Final answer:
The coordinates of points A and Q are (3, 5) and (7, 1) respectively. Without additional information or a third point, we cannot determine which point is between the other two. Understanding of positions within a coordinate system and transformations like rotation are key to these types of problems.
Step-by-step explanation:
The question relates to determining the position of points within a Cartesian coordinate system and to understanding concepts of relative position and coordinate transformations. The coordinates of point A are given as (3, 5) and point Q as (7, 1). Without the coordinates of a third point, we cannot determine which point is between the other two.
To address part c of the question, yes, the coordinates of A are (3, 5) and Q are (7, 1). This is a matter of reading and restating the given data. For the other parts of the question that relate to points and distances within different frames of reference, one typically needs additional points or information about the coordinate system to make further analysis.
For example, to answer part (c) regarding the invariance of the distance between points P and Q under rotations, one would demonstrate that distance formulas remain constant even when the axes are rotated, since distances are only dependent on the relative positions of the points, not the orientation of the coordinate system.