Find a point on the x-axis which is equidistant from the points A(7, 6) and B(-3, 4).

Question

Philoid · Accepted Answer

Let the point on x-axis be P(x, 0).

Given: Point P(x, 0) is equidistant from points A(7, 6) and B(-3, 4)

i.e., distance of P from A = distance of P from B

Squaring both sides,

⇒ (x – 7)² + 36 = (x + 3)² + 16

⇒ x² – 14x + 49 + 36 = x² + 6x + 9 + 16

⇒ –20x = –60

⇒ x = 3

Therefore, the point on the x-axis is (3, 0).