Question

If the points (2, 1) and (1, – 2) are equidistant from the point (x, y), show that x + 3y = 0.

Answer 1

(x, y) is equidistant from the points (2, 1) and (1, –2) 

⇒ Distance between (x, y) and (2, 1) = Distance between (x, y) and (1, –2)

⇒ \(\sqrt{(x-2)^2+(y-1)^2}\) = \(\sqrt{(x-1)^2+(y+2)^2}\)

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

⇒ – 4x + 2x – 2y – 4y = 0 ⇒ –2x – 6y = 0 ⇒ x + 3y = 0