Question

Suppose that receiving stations​ X, Y, and Z are located on a coordinate plane at the points ​(6​,2​), ​(negative 2​,negative 4​), and ​(negative 10​,4​), respectively. The epicenter of an earthquake is determined to be 5 units from X​, 5 units from​ Y, and 13 units from Z. Where on the coordinate plane is the epicenter​ located?

Answer 1

(2,-1)

Explanation:

A graph is useful here. Points X and Y have coordinate differences of ...

X -Y = (6, 2) -(-2, -4) = (6+2, 2+4) = (8, 6)

Then the distance between X and Y is ...

d = √(8² +6²) = √100 = 10

The point 5 units from X and from Y is the midpoint of XY:

E = (X +Y)/2 = ((6, 2) +(-2, -4))/2 = (4, -2)/2 = (2, -1)

The epicenter is (2, -1).

_____

The graph shows circles of radius 5 around X and Y, and a circle of radius 13 around Z. The circles intersect at the point (2, -1), the epicenter.