Mathematics

What is the locus of point that is equidistant from points P(1,3) and Q(3,5)?

What is the locus of point that is equidistant from points P(1,3) and Q(3,5)?
  • A.y = –χ + 6
  • B.y = –χ – 6
  • C.y = χ + 6
  • D.y = χ – 6
Correct Answer: Option A
Explanation

Locus of a point equidistant from two fixed points is the perpendicular bisector of the straight line joining the points Gradients of PQ = (5-3 / 3-1) = 2/2 = 1
Gradient bisector = -1
Equation of perpendicular bisector y – y1 = m(χ – χ1y – 4 = –χ + 2y = + 6