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JAMB Mathematics 2004 Question 31

Question 31

Coordinate Geometry

Find the value of α2 + β2 if α + β = 2 and the distance between the points (1, α) and (β, 1) is 3 units

  1. A.3
  2. B.5
  3. C.11
  4. D.14
Show the answer and explanation

Answer: C (11)

Explanation

(β − 1)2 + (1 − α)2 = 9 gives α2 + β2 − 2(α + β) + 2 = 9, so α2 + β2 = 9 + 4 − 2 = 11.