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.