Representation of moving reference frame as oblique coordinate system Why is the reference frame moving with respect to any stationary reference frame is represented by oblique coordinate system? 
 A: Extracts and Image Sources: Minkowski Diagrams Wikipedia

Space and time have properties which lead to different rules for the translation of coordinates in case of moving observers. In particular, events which are estimated to happen simultaneously from the viewpoint of one observer, happen at different times for the other.

Minkowski diagrams allow us to keep track of this with the mimium of equations.

In the Minkowski diagram this relativity of simultaneity corresponds with the introduction of a separate path axis for the moving observer. Following the rule described above each observer interprets all events on a line parallel to his path axis as simultaneous. The sequence of events from the viewpoint of an observer can be illustrated graphically by shifting this line in the diagram from bottom to top.
If $ct$ instead of $t$ is assigned on the time axes, the angle $α$ between both path axes will be identical with that between both time axes. This follows from the second postulate of the special relativity, saying that the speed of light is the same for all observers, regardless of their relative motion (see below). $α$ is given by

${\displaystyle \tan(\alpha )={\frac {v}{c}}=\beta }$.

Different scales on the axes.

The corresponding translation from $x$ and $t$ to $x′$ and $t′$ and vice versa is described mathematically by the so-called Lorentz transformation. Whatever space and time axes arise through such transformation, in a Minkowski diagram they correspond to conjugate diameters of a pair of hyperbolas. The scales on the axes are given as follows: If $U$ is the unit length on the axes of $ct$ and $x$ respectively, the unit length on the axes of $ct′$ and $x′$ is:

${\displaystyle U'=U\cdot {\sqrt {\frac {1+\beta ^{2}}{1-\beta ^{2}}}}}$.

The $ct$-axis represents the worldline of a clock resting in $S$, with $U$ representing the duration between two events happening on this worldline, also called theproper time between these events. Length $U$ upon the x-axis represents the rest length or proper length of a rod resting in $S$. The same interpretation can also be applied to distance $U′$ upon the $ct′-$ and $x′$-axis for clocks and rods resting in $S′$


Minkowski diagram with resting frame $(x, t)$, moving frame $(x′, t′)$, light cone, and hyperbolas marking out time and space with respect to the origin
