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"Cerca" is a form of "cerca", an adverb which is often translated as "close". "Está lejos" is a phrase which is often translated as "he's far". Learn more about the difference between "cerca" and "está lejos" below.
cerca(
sehr
-
kah
)An adverb is a word that describes a verb, an adjective, or other adverbs (e.g., to run quickly, very tired).
1. (not far)
a. close 
El hotel está realmente cerca, así mejor comemos allí.The hotel is really close, so let's just eat lunch there.
b. near 
Dice tu hermano que ya está cerca a la estación y que nos puede recoger.Your brother says he's near the station and that he can pick us up.
c. nearby 
Mi casa está cerca, pero te aviso que es un desastre.My house is nearby, but I have to warn you that it's a mess.
A feminine noun is almost always used with feminine articles and adjectives (e.g., la mujer bonita, la luna llena).
2. (enclosure)
a. fence  (of wood or wire)
Una casa con una cerca blanca simboliza el sueño americano.A house with a white fence symbolizes the American dream.
b. wall  (of stone or brick)
Ningún prisionero podría haber escalado las altas cercas de la cárcel.No prisoner could have scaled the high walls of the prison.
está lejos( 
ehs
-
tah
leh
-
hohs
)A phrase is a group of words commonly used together (e.g., once upon a time).
a. he's far  (masculine)
Extraño a Juan. Está lejos de casa, y no sé cuándo volverá.I miss Juan. He's far from home, and I don't know when he'll come back.
b. he's far away 
No creo que Pablo llegue a cenar. Está lejos y ya es tarde.I don't think Pablo will make it for dinner. He's far away, and it's late already.
c. she's far  (feminine)
¿Sabés dónde está Cecilia? - Está lejos, navegando en medio del mar.Do you know where Cecilia is? - She's far, sailing out in the ocean.
d. she's far away  (feminine)
Está lejos, en un país desconocido y se siente sola.She's far away, in an unknown country, and she feels lonely.
e. it's far 
La escuela está lejos de la estación y también está lejos de mi casa.The school is far from the station and it's far from my house too.
f. it's far away 
¿Sabes dónde queda la estación de trenes? - No, pero sé que está lejos.Do you know where the train station is? - No, I don't, but I do know it's far away.
h. is far away 
Tu casa está lejos. ¿Por qué no vamos a la mía?Your house is far away. Why don't we go to mine?
2. (formal) (are distant; second person singular)
A word or phrase used to refer to the second person formal “usted” by their conjugation or implied context (e.g., usted).
a. you're far 
Si está lejos de la estación de subte, le conviene tomar un taxi.If you're far from the metro station, you should take a taxi.
b. you're far away 
Ahora que está lejos, se da cuenta de lo importantes que son para usted sus amigos.Now that you're far away, you realize how important your friends are to you.
a. he's far 
Está lejos de ser un Adonis, pero es encantador de todos modos.He's far from being an Adonis, but he's charming anyway.
b. she's far 
Marta debería darse cuenta de que está lejos de ser buena cocinera.Marta should realize that she's far from being a good cook.
c. it's far 
El hotel no es caro, pero está lejos de ser un cinco estrellas.The hotel is not expensive, but it's far from being a five-star accommodation.
d. is far 
Ricardo está lejos de ser un tipo estricto; al contrario, es sumamente permisivo.Ricardo is far from being a strict guy; much to the contrary, he is overly permissive.
4. (formal) (are not at all; second person singular)
A word or phrase used to refer to the second person formal “usted” by their conjugation or implied context (e.g., usted).
a. you're far 
Usted está lejos de ser estúpido, así que no se deje engañar.You're far from stupid, so don't be fooled.