why does this sentence work: 「私が、それを使って文章を書いたところの、ペン」?

Question

So I've found this sentence:

私が、それを使って文章を書いたところの、ペン

And I'm wondering why it works. It's translated as "The pen that I used to write sentences with."

Shouldn't it be: "The pen that I used (it) and wrote sentences with", since 使う is in its te form meaning it's acting as and?

And why doesn't this sentence work?

私が、それを使って寿司を食べたところの、箸。

When I put it on google translate it translates as:

Chopsticks where I used them to eat sushi.

Why won't it translate to "Chopsticks that I used to eat sushi with"?

I found it from here on one of the answers to this question

Answer 1

You're correct that 使って is "use(d) and". if you need to translate sentences very faithfully like legal documents, the corresponding combinations of English and Japanese sentences would be as follows:

• 私が使って文章を書いたペン
  the pen I used and wrote sentences with
• 私が文章を書くために使ったペン
  the pen I used to write sentences with

Practically, however, there is little difference between these two, and this degree of deviation in translation is usually acceptable. For a learner who has acquired the basic grammar, it's important to learn to not worry about something like this too much.

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Some may be wondering how this ところの is working:

• 私がそれを使って文章を書いたところのペン
• 私がそれを使って寿司を食べたところの箸

These are actually correct and natural Japanese phrases, but at the same time, they are quite stilted and literary, and that's why Google Translate failed to translate them naturally (the natural version is shown at the beginning of my answer). A beginner should probably revisit this pattern much later after becoming able to solve JLPT N1-level problems.

Anyway, this type of ところの is something that is only sometimes inserted to emphasize (?) a relative clause:

1. 彼がやった行動
   彼がやったところの行動
   the action he took
2. 私が彼女に渡したプレゼント
   私が彼女に渡したところのプレゼント
   the present I gave to her
3. 昨日この道を通った人物
   (^?昨日この道を通ったところの人物)
   the person who passed this street yesterday
4. 海が見えるレストラン
   (^?海が見えるところのレストラン)
   the restaurant where you can see the ocean
5. 太陽が昇る時間
   (^?太陽が昇るところの時間)
   the time when the sun rises

The versions with ところの sound stilted, pompous, and politician-like to me, but there is no difference in meaning. This construction works especially well when the noun that has been pulled out is the object of the verb, as in your examples. In other types of relative clauses, like the ones I marked with ?, ところの sounds less natural, but they are not unheard of.

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EDIT: Here is another way in which ところの can be used naturally. The basic meaning of the phrase doesn't change with or without ところの, but I feel that ところの makes the modifying clause a little more reserved or euphemistic.

• 私が知っている相対性理論
  私が知っているところの相対性理論
  the theory of relativity as I understand it
• その哲学者が言う楽園
  その哲学者が言うところの楽園
  the "Paradise," as that philosopher calls it
• 日本人が信じる神
  日本人が信じるところの神
  the gods as believed in by the Japanese people

Answer 2

Re V-ru tokoro no: this locution arose from translation of English relative clauses into Japanese. Compare English, 'the line which is tangential to...', versus, 'the line such that it is tangential to...'.