How to Calculate the Distance Between Two Points in Algebra

In algebra, points are commonly defined using Cartesian coordinates. Coordinates "X" and "Y" of a point are given in brackets following the style (X, Y): for example (5,8). The distance formula based on the well-known Pythagorean theorem permits you to easily calculate the required distance from the differences of the coordinates of the two points. For instance, compute the distance between points with coordinates (-3.4, 6.5) and (2.7, 10.2).

Instructions

1. Calculate the difference between coordinates "X" of the points, and then raise the difference to the second power. In the example, it will be: (2.7 -(-3.4))^2 = 37.21.

2. Calculate the difference between coordinates "Y" of the points, and then raise the difference to the second power. In the example, it will be: (10.2 -6.5)^2 = 13.69.

3. Add up numbers obtained in step 1 and 2. In the example. the sum is 37.21 + 13.69 = 50.9.

4. Compute the square root of the sum (found in step 3) to find out the distance between the points. In our example, the distance (square root of 50.9) is 7.13 (rounded to the nearest hundredth).

References

• The Distance Formula
• Mathworld: Pythagorean Theorem