math algebra?

Suppose that receiving stations X, Y, and Z are located on a coordinate plane at the points (3 , 5), (-7 ,-6 ), and (-7 ,10 ), respectively. The epicenter of an earthquake is determined to be 5 units from X ,10 units from Y, and 10 units from Z. Where on the coordinate plane is the epicenter located?

1 Answer

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  • TomV
    Lv 7
    1 month ago

    If (x, y) is the epicenter of the earthquake, then:

    X: (x-3)² + (y-5)² = 25Y: (x+7)² + (y+6)² = 100Z: (x+7)² + (y-10)² = 100

    X₁: x² - 6x + y² - 10y = -9

    Y₁: x² + 14x + y² + 12y = 15

    Z₁: x² + 14x + y² - 20y = -49

    Y₁-Z₁: 32y = 64

    y = 2

    X₂: (x-3)² + (2-5)² = 25 → x² - 6x = 7

    Y₂: (x+7)² + (2+6)² = 100 → x² + 14x = -13

    Y₂-X₂: 20x = -20

    x = -1

    Answer: Epicenter at (-1, 2)

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