diff --git a/tests/unit/test_utils.py b/tests/unit/test_utils.py
index 28c47c8..b0e243c 100644
--- a/tests/unit/test_utils.py
+++ b/tests/unit/test_utils.py
@@ -1,9 +1,14 @@
 """Tests for flake8's utils module."""
+import os
+
 import pytest
 
 from flake8 import utils
 
 
+RELATIVE_PATHS = ["flake8", "pep8", "pyflakes", "mccabe"]
+
+
 @pytest.mark.parametrize("value,expected", [
     ("E123,\n\tW234,\n    E206", ["E123", "W234", "E206"]),
     ("E123,W234,E206", ["E123", "W234", "E206"]),
@@ -11,4 +16,26 @@ from flake8 import utils
     (["E123", "\n\tW234", "\n    E206"], ["E123", "W234", "E206"]),
 ])
 def test_parse_comma_separated_list(value, expected):
+    """Verify that similar inputs produce identical outputs."""
     assert utils.parse_comma_separated_list(value) == expected
+
+
+@pytest.mark.parametrize("value,expected", [
+    ("flake8", "flake8"),
+    ("../flake8", os.path.abspath("../flake8")),
+    ("flake8/", os.path.abspath("flake8")),
+])
+def test_normalize_path(value, expected):
+    """Verify that we normalize paths provided to the tool."""
+    assert utils.normalize_path(value) == expected
+
+
+@pytest.mark.parametrize("value,expected", [
+    ("flake8,pep8,pyflakes,mccabe", ["flake8", "pep8", "pyflakes", "mccabe"]),
+    ("flake8,\n\tpep8,\n  pyflakes,\n\n    mccabe",
+        ["flake8", "pep8", "pyflakes", "mccabe"]),
+    ("../flake8,../pep8,../pyflakes,../mccabe",
+        [os.path.abspath("../" + p) for p in RELATIVE_PATHS]),
+])
+def test_normalize_paths(value, expected):
+    assert utils.normalize_paths(value) == expected