Question

if a point on the x axis is equidistant from the points 2,-5 and -2,9 find its coordinates section formula

Answer 1

The coordinates of the point on the x-axis that is equidistant from the points (2,-5) and (-2,9) are (6.5, 0).

Step-by-step explanation:

The question asks for the coordinates of a point on the x-axis that is equidistant from the points (2,-5) and (-2,9). Since the point lies on the x-axis, its y-coordinate will be 0. To find the x-coordinate, set up an equation equating the distances from the point to (2,-5) and (-2,9), and solve for x.

Let the required point on the x-axis be (x,0). The distance from this point to (2,-5) is equal to the distance from this point to (-2,9).

√((x-2)^2 + (0--5)^2) = √((x+2)^2 + (0-9)^2)

Simplify the equation and solve for x:

1. (x-2)^2 + (-5)^2 = (x+2)^2 + (-9)^2
2. x^2 - 4x + 4 + 25 = x^2 + 4x + 4 + 81
3. 8x = 52
4. x = 6.5

Therefore, the coordinates of the point are (6.5, 0).