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?
1 answer:
Answer:
(2,-1)
Step-by-step 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.
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