Question

If the point P(x, y) is equidistant from the points A(5, 1) and B (1, 5), prove that x = y.

Answer 1

Coordinates are P(x, y), A(5, 1) and B (1, 5) 

Using distance formula = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

⇒ PA = PB

\(\sqrt{(x - 5)^2 + (y - 1)^2}\) = \(\sqrt{(x - 1)^2 + (y - 5)^2}\)

On squaring both sides, we get

(x -5)² + (y - 1)² = (x - 1)² + (y - 5)²

x² - 10x + 25 + y² - 2y + 1 = x² - 2x + 1 + y² - 10y + 25

- 8x + 8y = 0

x = y proved