What is an antipode?
Any point on the surface of a sphere, in this case the Earth, that lies diametrically opposite from a given point on the same surface, so that a line drawn between the two points through the center of the sphere forms a true diameter (e.g. through the Poles of a Sphere). The Antipodes islands of New Zealand, in the South Pacific, are named after this phenomenon because of there "closeness" to the antipodes of London.
The image below shows the relative distribution of landmasses on opposite sides of the Earth.
How can you calculate the antipodal point for any point on the Earth's surface?