Is this correct sentence structure/spelling?

el baño esta lejos de cocina. mi dormitorio esta cerca del baño.

El baño esta lejos de cocina.  Incorrect.

Correct sentence : El baño está lejos de la cocina. (written accent and definite, feminine article)

Translation: The bathroom is far from the kitchen.

Mi dormitorio esta cerca del baño. Incorrect.

Correct sentence : Mi dormitorio está cerca del baño. (written accent)

Translation: My bedroom is near the bathroom.

Explanation: Adverbs are words that have the function of complementing the meaning of the verb, an adjective or another adverb. "Cerca" and "Lejos" are adverbs of place whose function is to talk about the location where the action of the verb is being carried out and to specify that information, can be included in prepositional complements, where accompanied by a preposition and with the adverb as the core, a relationship is established with another element of the sentence whose location is already known.

"Cerca" + "de" + something whose location is already known.

"Lejos" + "de" + something whose location is already known.

In Spanish, if something already known is a noun, it needs a definite article "el" o "la" depends on the gender of the noun.

El baño está cerca de cocina. => It needs a definite article that agrees with the feminine gender of the noun "cocina", de + la

cerca de la cocina => prepositional complement to indicate where "baño" is.

Mi dormitorio está lejos del baño.=> "del" is a contraction that means "de + el"

Lejos del baño => prepositional complement to indicate where "dormitorio" is.