The correct option to complete the sentence "I saw you walking in that direction but I did not know exactly ...." is B. where you were going. Let's break down why this is the best choice and analyze the other options. Explanation of the Correct Answer (Option B)

1. Structure of the Sentence: The sentence is in the past tense ("I saw you walking"), which means that the clause that follows should also reflect this past context. The phrase "where you were going" maintains this past tense structure.
2. Subject-Verb Agreement: In the phrase "where you were going," "you" is the subject, and "were going" is the verb phrase in the past tense. This is grammatically correct and fits well with the main clause of the sentence.
3. Clarity and Naturalness: The expression "where you were going" is a natural way to ask about someone's destination in the past. It flows well and is commonly used in English.

Analysis of the Other Options Now, let's look at why the other options are incorrect or weaker:

• Option A: where are you going
• Tense Mismatch: This option uses the present tense "are," which does not match the past context established by "I saw you walking." The sentence would imply that the speaker is asking about the current destination, which is not what the original sentence conveys.
• Option C: where were you going to
• Unnecessary Preposition: While this option is grammatically correct, it is less concise than option B. The phrase "going to" is often used in informal speech, but in this context, it adds unnecessary complexity. The simpler "where you were going" is clearer and more direct.
• Option D: to where were you going
• Inverted Structure: This option uses an inverted structure that is more formal and less common in everyday conversation. The phrase "to where" is awkward and can confuse the reader. In standard English, we typically do not start a clause with a preposition followed by an inverted verb-subject order in this context.

Summary of Key Points

• The correct answer is B. where you were going because it maintains the past tense and is grammatically correct.
• Option A is incorrect due to a tense mismatch (present vs. past).
• Option C, while grammatically correct, is less concise and clear than option B.
• Option D is awkward due to its inverted structure and is not commonly used in conversational English.

Revision Summary

• The correct completion is B. where you were going.
• Ensure tense consistency in sentences; past actions should use past tense.
• Aim for clarity and conciseness in language; avoid unnecessary words.
• Familiarize yourself with common sentence structures to improve fluency in English.