Question

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

Answer 1

The point is on the x-axis,

⇒ the y coordinate is 0

Define x:

Let the point be (x , 0)

The point is equidistant from (7,6 ) and (3, 4)

Distance from (7, 6) to (x, 0) = (3, 4) to (x, 0)

Solve x:

(7 - x)² + 6²  = (3 - x)² + 4²

49 - 14x + x²  + 36 = 9 - 6x + x² + 16

x² - 14x + 85 = x² - 6x + 25

-8x = -60

x = 7.5

Find the point:

(x, 0) = (7.5, 0)

Answer: (7.5, 0)