The locus of a point P(x,y) such that PV = PW, where V = (1,1) and W = (3,5) is the perpendicular bisector of the line segment VW.

The midpoint of the line segment VW is given by the average of the coordinates of V and W:

Midpoint = ((1+3)/2, (1+5)/2) = (2, 3)

The slope of the line segment VW is given by the difference in y-coordinates divided by the difference in x-coordinates:

Slope of VW = (5-1)/(3-1) = 2

The slope of the perpendicular bisector is the negative reciprocal of the slope of VW:

Slope of perpendicular bisector = -1/2

Using the point-slope form of a line, we can find the equation of the perpendicular bisector:

y - 3 = (-1/2)(x - 2)

Multiplying both sides by 2, we get:

2y - 6 = -x + 2

Adding x and 6 to both sides, we get:

x + 2y = 8

So, the equation of the locus of a point P(x,y) such that PV = PW, where V = (1,1) and W = (3,5) is x + 2y = 8.