i am trying to extrude these vertices diagonally but with precision, just like when extrude along x or z etc... but how could it be done with the same precision when extruded along an axis? instead of going horizontally or vertically , i want to do it diagonally but i dont know how to do it
Once you've made your first extrusion, select the edge, open the Transform Orientations panel, click on the "+" button in order to create a new orientation that is aligned with your edge. Keep this new orientation selected in the panel and extrude along Y (EY).
In 2.79, at the bottom of the N panel (on the right of your 3D view, activate with N) > Transform Orientations, click on the "+" button:
Now the custom orientation is part of the Transform Orientations panel. After E for extrusion you'll need to press y twice though: