EXAMPLE 5Use graphs of circlesEARTHQUAKES The epicenter of an earthquake is the point on Earth'ssurface directly above the earthquake's origin. A seismograph can be used todetermine the distance to the epicenter of an earthquake. Seismographs areneeded in three different places to locate an earthquake's epicenter.Use the seismograph readings from locations A, B,and C to find the epicenter of an earthquake.• The epicenter is 7 miles away from A(-2, 2.5).• The epicenter is 4 miles away from B(4, 6).• The epicenter is 5 miles away from C(3, -2.5).SolutionThe set of all points equidistant from a givenpoint is a circle, so the epicenter is located oneach of the following circles.y-8BOA with center (-2, 2.5) and radius 7OB with center (4, 6) and radius 4AOC with center (3, -2.5) and radius 52To find the epicenter, graph the circles on agraph where units are measured in miles. Findthe point of intersection of all three circles.The epicenter is at about (5, 2).I.Why are three seismographs needed to locate an earthquake's epicenter?(Analyze Example #5 to help your thinking.)

Given that epicenter is 7 miles away from A-2,2.5. epicenter is 4 miles away from B4,6. epicenter is…

EXAMPLE 5 Use graphs of circles EARTHQUAKES 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. Use the seismograph readings from locations A, B, and C to find the epicenter of an earthquake. • The epicenter is 7 miles away from A(-2, 2.5). • The epicenter is 4 miles away from B(4, 6). • The epicenter is 5 miles away from C(3, -2.5).