Solve the problem.
-Suppose that receiving stations $X , Y$, and $Z$ are located on a coordinate plane at the points $( - 2,2 )$, $( - 14,10 )$, and $( - 10 , - 14 )$ respectively. The epicenter of an earthquake is determined to be 5 units from X, 15 units from $Y$, and 13 units from Z. Where on the coordinate plane is the epicenter located?
A) at $( - 6,0 )$
B) at $( - 4 , - 3 )$
C) at $( - 4 , - 2 )$
D) at $( - 5 , - 2 )$

Question

Quizplus · Accepted Answer

The epicenter's location can be found by solving the system of equations derived from the distances to each station. Using the distance formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ for each station and the given distances, only the coordinates $(-5, -2)$ satisfy all three conditions, making it the correct location of the epicenter.

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