The epicenter of the 9.0 magnitude quake was under the Indian Ocean near the west coast of the Indonesian island of Sumatra . . . (from “The Deadliest Tsunami in History?”)
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The epicenter refers to the point on the Earth's surface directly above the location where an earthquake originates. In the case of the 9.0 magnitude quake you mentioned, the epicenter was under the Indian Ocean near the west coast of the Indonesian island of Sumatra.
The epicenter of a 9.0 magnitude quake refers to the point on the Earth's surface directly above the location where the earthquake starts. To find the epicenter, scientists use data from seismographs located around the world. These devices record the seismic waves generated by the earthquake. By analyzing the arrival times of these waves at different stations, seismologists can triangulate the epicenter.
In the case of the 9.0 magnitude earthquake mentioned in your question, the epicenter was determined to be under the Indian Ocean near the west coast of the Indonesian island of Sumatra. This information was most likely obtained through seismographic data collected by various monitoring stations around the world.
So, to answer your question, the point of the Earth directly above the epicenter of the 9.0 magnitude quake would be the west coast of the Indonesian island of Sumatra, near the Indian Ocean.