Is it possible to locate an earthquake's epicenter using only one or two seismographs?
See solution.
Practice makes perfect
Seismographs are used to determine the distance to the epicenter of an earthquake. Since a seismograph has a shape of a circle, the epicenter should be somewhere on that circle. Suppose we want to find the epicenter of an earthquake using the seismographs readings from locations A, B, and C.
The epicenter is 7mi away from A(- 2,2.5).
The epicenter is 4mi away from B(4,6).
The epicenter is 5mi away from C(3,- 2.5).
Let's draw each of them separately and try to find the epicenter of the earthquake.
As we can see, knowing only one seismograph reading does not say too much about the location of the epicenter. Let's see what happens if we draw two seismograph readings together.
We see that two seismographs intercept at two points. The epicenter can be one of those two points. Again, we are not able to locate the epicenter of the earthquake. However, when three seismographs are drawn, they have only one common point.
This point is 7 miles from A, 4 miles from B, and 5 miles from C, so it is the epicenter. As a result, since it is not possible to find the epicenter using one or two seismographs, we need three seismographs.
