"My friend is down at the bottom of the room."
Translation:Tá mo chara thíos ag bun an tseomra.
Seomra takes the same form in both the nominative and the genitive. It can be identified as genitive in this sentence because it’s a masculine noun, and a definite masculine noun following an that begins with S + vowel gets a prefixed T only in the genitive. Thus, bun an tseomra means “the bottom of the room”.
Definite Genitive phrases only have one definite article in Irish, and it occurs between the nouns, not before the first one. ag bun an tseomra means "at the bottom of the room", fáinne geal an lae means "the dawning of the day", i lár na páirce means "in the middle of the field".
Remember that these English genitive phrases can also be restated as "the room's bottom" or "the day's dawning" or "the field's middle", where you only have one definite article.
Use of the two definite articles ("an") isn't accepted, for the reasons SatharnPHL explains below. But if you write "ag mbun an tseomra," Duolingo will accept the eclipsed form ("mbun"). [Edited to add:] Duolingo does say that "mbun" is a typo. I'm not advanced enough in Irish to know why "bun" is not eclipsed after "ag" in this sentence. Hopefully one of the experts will weigh in on this point.
thíos is a position - Tá sé thíos i bpoll - "He's down in a hole", Tá sé thíos faoin talamh - "It's (down) under the ground".
anuas (no fada) indicates motion - ag teacht anuas ón díon - "coming down from the roof", Leag anuas ar an mbord é - "set it down on the table".