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A water pipeline runs straight from a pumping station P(-5, 2) to a village tank T(10, 12) on a survey grid marked in kilometres.
A pressure valve is fitted at the point dividing PT in the ratio 2 : 3 measured from P.
Where is the valve?

Class 10Section FormulaGeometry — Coordinates
  • A(1, 6)
  • B(4, 8)
  • C(2.5, 7)
  • D(1, 5)

Step-by-Step Solution

and , so the valve is at (1, 6). (4, 8) applies the ratio as 3 : 2, i.e. measured from T instead of from P; (2.5, 7) is the midpoint, which ignores the 2 : 3 split; (1, 5) divides 30 by 6 instead of by .
Answer: A) (1, 6)

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