The locus of a point P(x,y) such that PV = PW where V = (1,1) and W = (3,5). This means that the point P moves so that its distance from V and W are equidistance.
PV = PW
\(\sqrt{(x-1)^{2} + (y-1)^{2}} = \sqrt{(x-3)^{2}
+ (y-5)^{2}}\).
Squaring both sides of the equation,
(x-1)² + (y-1)² = (x-3)² + (y-5)².
x²-2x+1+y²-2y+1 = x²-6x+9+y²-10y+25
Collecting like terms and solving, x + 2y = 8.