C# collection of two points doesn't return any results

Question

Class:

public class Point : IEqualityComparer<Point>
{               
    public char HorizontalPosition { get; set; }
    public int VerticalPosition { get; set; }

    public Point(char horizontalPosition, int verticalPosition)
    {
        HorizontalPosition = char.ToUpper(horizontalPosition);
        VerticalPosition = verticalPosition;           
    }   

    public bool Equals(Point x, Point y)
    {
        return (x.VerticalPosition == y.VerticalPosition && x.HorizontalPosition == y.HorizontalPosition);
    }

    public int GetHashCode(Point obj)
    {
        return (obj.HorizontalPosition.GetHashCode() + obj.VerticalPosition.GetHashCode());
    }
}

I am trying to find common Points (intersection) in two collections, but the result is empty collection - two elements should be in it. Why? I've implemented IEqualityComparer. Did I did something wrong?

Example collections:

  List<Point> first = new List<Point> { new Point('a', 1), new Point('b', 2) };
  List<Point> second = new List<Point> { new Point('a', 1), new Point('b', 2) };
  List<Point> intersection = first.Intersect(second).ToList();

Intersection is empty list, but two elements should be in it.

Answer 1

List<Point> first = new List<Point> { new Point('a', 1), new Point('b', 2) };
            List<Point> second = new List<Point> { new Point('a', 1), new Point('b', 2) };
            List<Point> intersection = first.Intersect(second, new PointComparer()).ToList();


public class Point 
{
    public char HorizontalPosition { get; set; }
    public int VerticalPosition { get; set; }

    public Point(char horizontalPosition, int verticalPosition)
    {
        HorizontalPosition = char.ToUpper(horizontalPosition);
        VerticalPosition = verticalPosition;
    }
}

public class PointComparer : IEqualityComparer<Point>
{
    public bool Equals(Point x, Point y)
    {
        return (x.VerticalPosition == y.VerticalPosition && x.HorizontalPosition == y.HorizontalPosition);
    }

    public int GetHashCode(Point obj)
    {
        return (obj.HorizontalPosition.GetHashCode() + obj.VerticalPosition.GetHashCode());
    }
}

Try above example