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A mobile tower stands at the origin and its signal reaches every point within 10 km. Four subscribers live at A(6, 7), B(-9, 1), C(3, 9) and D(7, -8).
Which subscriber is OUTSIDE the signal range?

Class 10Distance FormulaGeometry — Coordinates
  • AC(3, 9)
  • BD(7, -8)
  • CB(-9, 1)
  • DA(6, 7)

Step-by-Step Solution

Compare each squared distance with . A gives 36 + 49 = 85, B gives 81 + 1 = 82, C gives 9 + 81 = 90 and D gives 49 + 64 = 113. Only D exceeds 100, so D is km away and out of range; the other three are all a little under 10 km. B looks the most distant because of the -9, but a negative coordinate is squared and does not increase the distance.
Answer: B) D(7, -8)

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