Practice Distance Formula in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

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

Imagine two points on a grid. Draw a horizontal line from one and a vertical line from the other to form a right triangle. The horizontal leg is the difference in x-coordinates, the vertical leg is the difference in y-coordinates, and the hypotenuse—the direct distance—comes from the Pythagorean theorem. The distance formula is just a^2 + b^2 = c^2 in coordinate clothing.

Example 1

easy
Find the distance between the points (1, 2) and (4, 6).

Example 2

medium
Find the distance between (-3, 5) and (2, -7).

Example 3

medium
Show that the triangle with vertices A(0, 0), B(3, 4), and C(6, 0) is isosceles.

Example 4

medium
Find the points on the x-axis that are 5 units away from the point (2, 4).