Question

1. Draw a cartoon related to the sentence.

2. Draw a cartoon relating to the sentence.

3. Draw a cartoon and write down a sentence related to it below.

4. Draw a cartoon and write dwon a sentence related to it below.

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Are the sentences above grammatical?
Do we have to use 'related' or 'relating'?

Answer 1

They are all OK. The first and third are the best. The fourth has a spelling error (or typo).

The sentence related to the cartoon or photo or picture is called a caption. You could write this:

<i>Draw a cartoon and a caption below it.</i>

Answer 2

4. Draw a cartoon and write down a sentence relating to it below.

Thank you. #4 should be like this.

Do you mean we can use both 'related' and 'relating'?

Answer 3

Yes, you can. There's not much difference between them; mostly the difference is in the participial form (present or past), not in meaning.