C++ :: Synthesized Default Constructor

A compiler auto created default constructor is called a synthesized default constructor. It will initialize the built-in members to 0 or not depends on where the class object is defined? if I define a class

class point{
public:
double x, y;
};

if I define point point1; in global scope then point1.x and point1.y will be initialized to 0, if I define point point2; in a local scope, then its x and y won't be initialized? If it is like this, then I believe if there are built-in type members in a class, then the synthesized default constructor is almost useless!