The epicenter of an earthquake is the point on Earth’s surface directly above the earthquake’s origin. A seismograph can be used to determine the distance to the epicenter of an earthquake. Seismographs are needed in three different places to locate an earthquake’s epicenter. Find the location of the earthquake’s epicenter if it is 3 miles away from A(2,3)A(2,3), 4 miles away from B(−5,3)B(−5,3), and 5 miles away from C(−1,−2)C(−1,−2).
You could do it graphically as follows:
Alternatively, you could do it algebraically by letting the epicenter have coordinates (x, y) and then using Pythagoras to express the distance between (x, y) and any two of the given points to find x and y (you only need two of the points because you only need to find two unknowns).