Question

Suppose that receiving stations X, Y, and Z are located on a coordinated plane at the points (12,6), (-12,-4), and (-6,9), respectively. The epicenter of an earthquake is determined to be 13 units from X, 13 units from Y, and 10 units from Z. Where on the coordinate plane is the epicenter located?

a) (0, 0)
b) (8, 5)
c) (-5, -2)
d) (10, 7)

Answer 1

The location of the epicenter on a coordinate plane requires finding the intersection of three circles centered at points X, Y, and Z with respective radii of 13, 13, and 10 units. None of the provided answer options match the criteria.

Step-by-step explanation:

The student is asking where the epicenter of an earthquake is located on a coordinate plane given the distances from three different points (X, Y, and Z). This problem can be solved using the concept of circles in a coordinate plane, where each circle represents the set of all points that are at a given distance from a single point (the center).

To find the epicenter, we need to determine where the circles with centers at X (12,6), Y (-12,-4), and Z (-6,9) and radii of 13, 13, and 10 units, respectively, intersect. By analyzing the given coordinates and distances, we can identify the point where all three circles intersect. Through calculation or graphical representation, we find that none of the points (0, 0), (8, 5), (-5, -2), or (10, 7) are equidistant from X, Y, and Z. Therefore, none of the options given are correct for the location of the epicenter.