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

The locus of a point that is equidistant from two given points is the perpendicular bisector of the line segment connecting those two points. In this case, the two points are P(1,3) and Q(3,5). To find the perpendicular bisector of the line segment PQ, we can first find the midpoint of PQ: Midpoint = ( (1+3)/2 , (3+5)/2 ) = (2,4) Next, we can find the slope of the line PQ: Slope of PQ = (5-3) / (3-1) = 1 The perpendicular bisector of PQ will have a slope that is the negative reciprocal of the slope of PQ, which is -1. Therefore, we can use the point-slope form of a line to find the equation of the perpendicular bisector, using the midpoint (2,4) and slope -1: y - 4 = -1(x - 2) Simplifying this equation, we get: y = -x + 6 So the equation of the locus of points that are equidistant from P and Q is y = -x + 6. Therefore, the correct option is: - y = -x + 6