Question

If the distances of the points P(x , y) from (1, 0) and (0, 1) are equal, then which of the following is ______.

Options

• x + y = 0

• x = y + 1

• y = x + 1

• x = y

Answer 1

If the distances of the points P(x, y) from (1, 0) and (0, 1) are equal, then which of the following is x = y.

Explanation:

Let the points be A (1, 0) and B (0, 1).

Given that the distance of the point P(x, y) from (1, 0) and (0, 1) is equal.

∴ PA = PB

∴ PA² = PB²

∴ (x − 1)² + (y − 0)² = (x − 0)² + (y − 1)²

∴ x² + 1 − 2x + y² = x² + y² + 1 − 2y

∴ 1 − 2x = 1 − 2y

∴ −2x = −2y

∴ x = y