How to find local point of children


I want to find a point (bottomPoint1), which is always located 30 cm in front of a ladder when the player approaches it. It should be approximately in the position, where I have drawn here:

Looks an easy task but I can’t figure it out. Partially maybe therefore, because the inspector shows the local position, but global “direction”. Meaning, the position NUMBERS look good, but when I move a ladder forward - according to the editor view I pull on the Y-axis, but the inspector says, that I am pulling the X-axis. I already got the info, that the inspector shows the directions of the parent. Which is super confusing for me. If somebody can tell me, why it is set like this, I would appreciate it. Cause I would expect, that if I pull on the Y-Axis, that also the inspector shows, that I am pulling the Y-axis. I have now tried different variants of getting local / global positions, but nothing works. My last code is:

bottomPoint1 = new Vector3(ladder1Position.x - 0.3f, ladder1Position.y + 0.03f, ladder1Position.z);

I am getting this incorrect result:

The problem is, that unity is taking the global direction, not the local ones of the ladders.
So how can I get the local direction of the ladders?

Thank you

Found it out:

Vector3 bottomPoint1 = ladder1Position + ladder1.up * 0.3f;