Question

The point P on x-axis equidistant from the points A(–1, 0) and B(5, 0) is ______.

Options

• (2, 0)

• (0, 2)

• (3, 0)

• (2, 2)

Answer 1

The point P on x-axis equidistant from the points A(–1, 0) and B(5, 0) is (2, 0).

Explanation:

Let the position of the point P on x-axis be (x, 0), then

PA² = PB²

⇒ (x + 1)² + (0)² = (5 – x)² + (0)²

⇒ x² + 2x + 1 = 25 + x² – 10x

⇒ 2x + 10x = 25 – 1

⇒ 12x = 24

⇒ x = 2

Hence, the point P (x, 0) is (2, 0).