Question

Write the coordinates of a point P on x-axis which is equidistant from the point A(–2, 0) and B(6, 0).

Answer 1

Given: A(–2, 0), B(6, 0). Let P be on the x-axis so P(x, 0).

Distance PA = |x – (–2)| = |x + 2|.

Distance PB = |x – 6|.

Equate: |x + 2| = |x – 6|.

Solve: either x + 2 = x – 6 (impossible)

or x + 2 = –(x – 6)

⇒ x + 2 = –x + 6

⇒ 2x = 4

⇒ x = 2

The required point is P(2, 0).