How do u find the coordinates of the epicenter?
Jun 30, 2009
in
Earthquake Questions
After an earthquake, you are given seismograph reading from three locations, where the coordinate units are miles
At A(2, 1), the epicenter is 5 miles away
At B(-2, -2), the epicenter is 6 miles away.
At C(-6, 4), the epicenter is 4 miles away.
a) What are the coordinates of the epicenter?
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2 comments
Jessica on June 30, 2009 at 1:45 pm
Let E(h, k) be the epicenter.
AE² = [(h - 2)² + (k - 1)²] = 25
h² + k² – 4h – 2k = 20……(eqn 1)
BE² = [(h + 2)² + (k + 2)²] = 36
h² + k² + 4h + 4k = 28……(eqn 2)
CE² = [(h + 6)² + (k - 4)²] = 16
h² + k² + 12h – 8k = -36……(eqn 3)
Solving eqn(1) & eqn(2), we get 4h + 3k = 4…….(eqn 4)
Solving eqn(2) & eqn(3), we get 2h – 3k = -16……(eqn 5)
Solving eqn(4) & eqn(5), we get h = -2, k = 4.
So the coordinates of epicenter are (-2, 4).
Andrea Decker on October 18, 2010 at 1:41 pm
How did you get equations 4 & 5? How did you solve 1& 2, and 2 & 3 to get those answers? Please explain
.