Distance Formula Math Example 4

Follow the full solution, then compare it with the other examples linked below.

medium

Find the points on the

x

-axis that are

5

units away from the point

(2, 4)

1
Any point on the $x$ -axis has coordinates $(x, 0)$ . Use the distance formula: $\sqrt{(x-2)^2 + (0-4)^2} = 5$ .
2
Square both sides: $(x-2)^2 + 16 = 25$ , so $(x-2)^2 = 9$ .
3
Take square roots: $x - 2 = \pm 3$ , so $x = 5$ or $x = -1$ .

Answer

(-1, 0) \text{ and } (5, 0)

Distance-formula problems can be used to locate unknown points, not just measure known ones. Restricting the point to the

x

-axis fixes one coordinate and leaves an equation in the other.

About Distance Formula

A formula for finding the distance between two points in the coordinate plane, derived directly from the Pythagorean theorem.

Find the distance between the points [formula] and [formula].

Find the distance between [formula] and [formula].

Show that the triangle with vertices [formula], [formula], and [formula] is isosceles.