The coordinates of the foot of the perpendicular from (0, 0) upon the line x + y = 2 are

A line through the point A(2, 0) which makes an angle of 30$$^\circ$$ with the positive direction of x-axis is rotated about A in clockwise direction through an angle 15$$^\circ$$. Then the equation of the straight line in the new position is

If C is the reflection of A(2, 4) in x-axis and B is the reflection of C in y-axis, then $$|AB|$$ is

The number of points on the line x + y = 4 which are unit distance apart from the line 2x + 2y = 5 is