How to Use a Distance Formula for Geometry

The distance formula stems from the Pythagorean Theorem and is primary used to calculate separation between any two points that are given in Cartesian coordinates. According to the formula the distance equals to sqrt((X2 - X1)^2 + (Y2 - Y1)^2); X1,Y1 and X2,Y2 are Cartesian coordinates of the two points and "sqrt" is an abbreviation for the root square math operation. It is also possible to compute a geometrical shape perimeter, for example, the circle circumference based on the distance formula.

Difficulty: Easy

Instructions

Things You'll Need:

• Calculator

Calculating a distance between two points

1. Subtract the coordinate "X" of the first point from the coordinate "X" of the second point, and raise the difference to the power of 2. For example, the two points have Cartesian coordinates as follows: (4.1, -3.65) and (6.7, 10.67).
   In this example, it will be: (6.7 -- 4.1)^2 = 6.76.

2. Subtract the coordinate "Y" of the first point from the coordinate "X" of the second point, and raise the difference to the power of 2.
   In our example, it will be: (10.67 - ( - 3.65))^2 = 205.06. Note that the result is rounded to hundredth

3. Add up values from Step 1 and 2, and then take the square root to calculate the distance between two points. In this example, the distance = sqrt(6.76 + 205.06) = sqrt (211.82) = 14.55 (rounded to hundredth).

Calculating circumference for a circle

4. Subtract the coordinate "X" of the circle center from the coordinate "X" of a circle point. Then raise the difference to the power of 2. For instance, the circle center has Cartesian coordinates (4.5, 2.8), while coordinates of a point on the circle are (-1, 1.4).
   In this example, it will be: (-1, -- 4.5)^2 = 30.25.

5. Subtract the coordinate "Y" of the circle center from the coordinate "Y" of a circle point. Then raise the difference to the power of 2. In our example, it is (1.4 - 2.8)^2 = 1.96.

6. Add up values from Step 1 and 2, and then take the square root of the sum to calculate the radius of the circle. In this example, the radius = sqrt(30.25 + 1.96) = sqrt (32.21) = 5.67. Note that the result is rounded to hundredth.

7. Multiply the radius (Step 3) by "2" and the number 3.1416 to calculate the circumference length. In our example, the circumference = 5.67 x 2 x 3.1416 = 35.63.

References

• "The Distance Formula," Elizabeth Stapel, Purplemath.com.