Question

Suppose that receiving stations X, Y, and Z are located on a coordinate plane at the points (9, 8), (-3, -8), and (-9, 5), respectively. The epicenter of an earthquake is determined to be d units from X, e units from Y, and f units from Z. Where on the coordinate plane is the epicenter located?

a) d units from X, e units from Y, and f units from Z.

b) e units from X, d units from Y, and f units from Z.

c) f units from X, e units from Y, and d units from Z.

d) e units from X, f units from Y, and d units from Z.

Answer 1

To find the location of the epicenter, add the distances to the x and y coordinates of each station to find the coordinates of the epicenter. The correct option is (a) d units from X, e units from Y, and f units from Z.

Step-by-step explanation:

To find the location of the epicenter, we need to determine the coordinates on the coordinate plane. Let's suppose the epicenter is d units from X, e units from Y, and f units from Z. We can add the distances to the x and y coordinates of each station to find the coordinates of the epicenter. Here are the steps:

1. Add d to the x-coordinate of X, which is 9. The new x-coordinate is 9 + d.
2. Add e to the x-coordinate of Y, which is -3. The new x-coordinate is -3 + e.
3. Add f to the x-coordinate of Z, which is -9. The new x-coordinate is -9 + f.
4. Add d to the y-coordinate of X, which is 8. The new y-coordinate is 8 + d.
5. Add e to the y-coordinate of Y, which is -8. The new y-coordinate is -8 + e.
6. Add f to the y-coordinate of Z, which is 5. The new y-coordinate is 5 + f.

The coordinates of the epicenter are (9 + d, 8 + d). So, the correct option is (a) d units from X, e units from Y, and f units from Z.