Which pair of points forms a vertical line segment that is 4 units long?

In a Cartesian coordinate system, a vertical line segment always is parallel to the y-axis, so we have this coordinate system in the figure below. We need to find a pair of points that is 4 units long.

So, this pair of points are in the general forms as follow:




Given that the straight line is vertical, then:


 
Then the point 2 is modified as:



We need to find a point which is 4 units long, so:


∴

So, we can find infinite points given a value of , therefore if:

then:

∴

Thus, if then a pair of points are: