Step 1: Recall the condition for optical activity.
A molecule is optically active if it contains a chiral carbon atom attached to four different groups.
Step 2: Examine glycine.
The structure of glycine is
\[
NH_2-CH_2-COOH
\]
The \(\alpha\)-carbon is attached to
\[
H,\ H,\ NH_2,\ COOH
\]
Since two substituents are identical (\(H\) and \(H\)), the carbon atom is not chiral.
Therefore, glycine is optically inactive.
Step 3: Examine the remaining amino acids.
Alanine:
\[
NH_2-CH(CH_3)-COOH
\]
contains a chiral carbon.
Tyrosine and proline also contain asymmetric carbon atoms and are optically active.
Step 4: Final conclusion.
Hence, the optically inactive amino acid is
\[
\boxed{\text{Glycine}}
\]
Therefore, the correct option is (1).