Find the equation of the locus of a point P(x,y) such that PV = PW, where V = (1,1) and W = (3,5)

Answer Details

To find the locus of point P(x,y) such that PV = PW, we need to find the set of all points that are equidistant from V(1,1) and W(3,5). First, we can find the distance between V and W using the distance formula: d = sqrt((3-1)^2 + (5-1)^2) = sqrt(20) The midpoint M of line segment VW is: M = ((1+3)/2, (1+5)/2) = (2,3) Using the midpoint formula, we can find the equation of the perpendicular bisector of VW, which is the locus of points equidistant from V and W: (y - 3) = -(1/2)(x - 2) 2y - 6 = -x + 2 x + 2y = 8 Therefore, the correct option is (D) x + 2y = 8.