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
easyFind the distance between the points (1, 2) and (4, 6).
Example 2
mediumFind the distance between (-3, 5) and (2, -7).
Example 3
mediumShow that the triangle with vertices A(0, 0), B(3, 4), and C(6, 0) is isosceles.
Example 4
mediumFind the points on the x-axis that are 5 units away from the point (2, 4).