Geometry (C10)

Find the linear relation between x and y such that P(x, y) is equidistant from the points A(1, 4) and B(–1, 2).

Answer

PA = PB

⇒ PA2 = PB2

⇒ (x – 1)2 + (y – 4)2 = (x + 1)2 + (y – 2)2

⇒ x2 + 1 – 2x + y2 + 16 – 8y = x2 + 1 + 2x + y2 + 4 – 4y

⇒ x + y – 3 = 0