JAMB 2017 · UTME (set 2) · Q38

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

Worked solution (try it first)

$PV = PW$ , so square both distances: $(x - 1)^2 + (y - 1)^2 = (x - 3)^2 + (y - 5)^2$ .
Expand, and cancel $x^2$ and $y^2$ : $-2x + 1 - 2y + 1 = -6x + 9 - 10y + 25$ .
Collect terms: $4x + 8y = 32$ .
Divide by 4: $x + 2y = 8$ , option D.