Which point on the x-axis is equidistant from the points A(7, 6) and B(-3, 4)?

Question

Philoid · Accepted Answer

⇒ Point on x-axis means its y-coordinate is zero.

⇒ Let the point be P(x, 0)

Using the distance formula,

⇒

⇒ Distance AP = Distance BP

⇒ (x-7)² + (0-6)² = (x + 3)² + (0-4)²
⇒ x² + 49-14x + 36 = x² + 9 + 6x + 16

⇒ 49-9 + 36-16 = 6x + 14x

⇒ 40 + 20 = 20x

⇒ x = 60/20

x = 3

Therefore the coordinate of P is (3,0).