When should I use a define article before directions?

Question

I drew a map of Iran without looking at it. Then I checked my drawing with the real map, and made this statement:

I knew there is a slope in the western borders but I didn’t know the details. For the eastern border, I should have pulled it more toward south-east. Mine is very straight.

• is it south-east or the south-east? I think since the directions are a limited and specific set, it needs "the".
  • should I use "border" or "borders" in the first or second case?

Answer 1

The object of towards is a thing or place, not a direction, hence "the southeast", the region.

The army marched towards the southeast. ^sector

The army marched southeast. ^vector

The army marched towards southeast ^{ungrammatical}

You cannot move towards the-direction-in-which-you-are-moving. You are moving in that direction. A direction of movement is a vector, not a sector.

Answer 2

When you refer to the points of the compass as to a direction then you don't need the article in general. However, there may be situations where you will have to include it. When you refer to the points of the compass as to locations or dimensions then you need the article in most cases (practically in all cases).

• I went south. (direction)
• I went to the south. (location)
• The station is 5km northeast of here. (direction)
• I was travelling from the east to the west. (location)

Mind, you don't usually spell ordinal point with a hyphen: northeast, southeast, southwest, northwest.

P.s. In general "border" when speaking about the boundaries of anything is used in the singular form represented as a single closed line. However, when split into section we can still represent a particular section as a border or as individual borders.

• They've crossed the border of the country. (single closed line)
• They've crossed the western border of the country. (The section in western part of the country)