Select the correct active form of the given sentence.

Luckily, the machinery was not used by them.

Luckily, they did not used the machinery.

The correct active form of the given sentence "Luckily, the machinery was not used by them" is Luckily, they did not use the machinery.

The passive voice of the sentence is "Luckily, the machinery was not used by them." This sentence is in the simple past tense, which is used to describe an action that happened in the past. The passive voice of the sentence is formed by putting the subject of the active sentence after the verb "to be" and the past participle of the main verb. In this case, the subject of the active sentence is "the machinery" and the main verb is "use." The past participle of "use" is "used." So, the passive form of the sentence is "Luckily, the machinery was not used by them."

The active voice of the sentence is formed by putting the subject of the passive sentence before the verb and removing the word "by." In this case, the subject of the passive sentence is "they," and the verb is "use." So, the active form of the sentence is "Luckily, they did not use the machinery."

The other options are incorrect because:

• Luckily, they had not used the machinery." This sentence is in the past perfect tense, which is used to describe an action that happened in the past before another action happened. However, there is no other action mentioned in the sentence.
• Luckily, they did not used the machinery." This sentence is in the simple past tense, but the verb "used" is in the wrong form. The correct form of the verb is "did not use."
• Luckily, they have not used the machinery." This sentence is in the present perfect tense, which is used to describe an action that has happened in the past and is still relevant to the present. However, the action of not using the machinery is not relevant to the present.
• Luckily, I did not used the machinery." This sentence is in the simple past tense, but the subject of the sentence is incorrect. The subject of the sentence should be "they."