Answer:
To find the epicenter of an earthquake, you need to use the distances from at least three seismograph stations to the earthquake. You can draw a circle around each station with a radius equal to the distance to the earthquake. The point where the three circles intersect is the epicenter.
In your case, you have the coordinates of three stations (x, y, and z) and the distances from each station to the earthquake (13, 10, and 10 units). You can use a formula to find the coordinates of the epicenter, or you can use a graphing tool to plot the circles and find their intersection.
One possible formula to find the epicenter is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) are the coordinates of the epicenter, and r is the distance from a station to the epicenter. You can plug in the values for x, y, and r for each station and get three equations. Then you can solve them simultaneously to find h and k.
Alternatively, you can use a graphing tool like [Desmos] to plot the circles and find their intersection. You can enter the equations for each circle in the form:
(x - a)^2 + (y - b)^2 = c^2
where (a, b) are the coordinates of a station, and c is the distance from that station to the earthquake. For example, for station x, you can enter:
(x - 10)^2 + (y - 4)^2 = 169
You can do the same for stations y and z. Then you can zoom in on the graph and see where the three circles intersect. You can also click on the intersection point to see its coordinates.
Using either method, you should get that the epicenter is located at approximately (-1.6, -0.4) on the coordinate plane. You can check your answer by measuring the distance from this point to each station and seeing if it matches with the given distances.