EdgeCollider2D for the same points as LineRenderer has different position

I have trouble of understanding world space vs local space in my LineRenderer and EdgeCollider2D components.

I have a player GO with attached LineRenderer and EdgeCollider2D to it. I have a helper variable to store my moves as a following list:

 private List<Vector3> _moveLinePoints;

Then in my update method I'm filling player's position as following:

 _moveLinePoints.Add(playerPosition.position);

Then I set up my line renderer with those points and also my edge collider:

 _lineRenderer.positionCount = _moveLinePoints.Count;
 _lineRenderer.SetPositions(_moveLinePoints.ToArray());

 var vector2Points = _moveLinePoints
             .Select(point => new Vector2(point.x, point.y))
             .ToList();

 _edgeCollider.points = vector2Points.ToArray();

My line renderer has useWorldSpace set to true because if it's not it has some strange offset (so I assume that playerPosition.position are world coordinates, right?)

When I run my game I see Liner Renderer with correct position and my collider with wrong position:

How can I change my EdgeCollider points to be world space related?