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: y = -χ + 6
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 - χ1
y - 4 = -χ + 2
y = -χ + 6
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 - χ1
y - 4 = -χ + 2
y = -χ + 6