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JAMB Mathematics 1995 Question 31

Question 31

Loci

P is on the locus of point equidistant from two given points X and Y. UV is a straight line through Y parallel to the locus. If ∠PYU is 40°, find ∠XPY

  1. A.100°
  2. B.80°
  3. C.50°
  4. D.40°
Show the answer and explanation

Answer: B (80°)

Explanation

The locus is the perpendicular bisector of XY, and it bisects angle XPY. UV is parallel to it, so angle PYU equals the angle between PY and the bisector (alternate angles) = 40°. So angle XPY = 2 × 40° = 80°.