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P and Q lie on the segment joining A(-2, -5) and B(10, 7), with AP : PB = 1 : 5 and AQ : QB = 5 : 1.
Which statement gives both points correctly?

Class 10Section FormulaGeometry — Coordinates
  • AP(0, -3) and Q(8, 5)
  • BP(8, 5) and Q(0, -3)
  • CP(2, -1) and Q(6, 3)
  • DP(0, -3) and Q(4, 1)

Step-by-Step Solution

For P with ratio 1 : 5: and , so P(0, -3). For Q with ratio 5 : 1: and , so Q(8, 5). The second option attaches each ratio to the wrong point; the third uses 1 : 2 and 2 : 1 instead of 1 : 5 and 5 : 1; the last replaces Q by the midpoint (4, 1) of AB.
Answer: A) P(0, -3) and Q(8, 5)

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