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JAMB Mathematics 1999 Question 30

Question 30

Loci

Find the equation of the locus of a point P(x, y) such that PV = PW, when V = (1, 1) and W = (3, 5).

  1. A.2x + 2y = 9
  2. B.2x + 3y = 8
  3. C.2x + y = 9
  4. D.x + 2y = 8
Show the answer and explanation

Answer: D (x + 2y = 8)

Explanation

P lies on the perpendicular bisector of VW. The midpoint is (2, 3) and VW has gradient 2, so the bisector has gradient −1/2: y − 3 = −½(x − 2), i.e. x + 2y = 8.