How to Find the Distance Between Two Points: 6 Steps

2023 Author: Sybil Carroll | [email protected]. Last modified: 2023-05-21 06:08

The distance between two points can be thought of as a line. To find the length of this line, you can use the distance formula: √ (x2 − x1) 2+ (y2 − y1) 2 { displaystyle (x2-x1) ^ {2} + (y2-y1) ^ {2 }}

Pasos

Step 1. Obtain the coordinates of the two points between which you are going to calculate the distance

Call the first point (x₁, and₁) and call the second (x₂, and₂). It is not vitally important to know what point each is, as long as you maintain consistency between labels (1 and 2) throughout the problem.

• x₁ is the horizontal coordinate (that is, along the x axis) of point 1 and x₂ is the horizontal coordinate of point 2. and₁ is the vertical coordinate (along the y axis) of point 1 y y₂ is the vertical coordinate of point 2.
• As an example, imagine that you have the points (3, 2) and (7, 8). If (3, 2) is (x₁, and₁), then (7, 8) will be (x₂, and₂).

Step 2. Learn to use the distance formula

This formula is used to find the length of a line that extends between two points: that is, point 1 and point 2. The linear distance is equal to the square root of the square of the horizontal distance plus the square of the vertical distance between two points. In simpler terms, it is the square root of: (x2 − x1) 2+ (y2 − y1) 2 { displaystyle (x2-x1) ^ {2} + (y2-y1) ^ {2}}

Step 3. Find the vertical and horizontal distance between the points

First, subtract and₂ - and₁ to find the vertical distance. Then subtract x₂ - x₁ to find the horizontal distance. Don't worry if the subtraction results in a negative number. The next step will be to square the result and the square of a number is always a positive integer.

• Find the distance along the y-axis. For the example points (3, 2) and (7, 8), where (3, 2) is point 1 and (7, 8) is point 2: (and₂ - and₁) = 8 - 2 = 6. This means that, between these two points, there are six units of distance along the y-axis.
• Find the distance along the x-axis. For the same points in the example (3, 2) and (7, 8): (x₂ - x₁) = 7 - 3 = 4. This means that, between these two points, there are four units of distance along the x-axis.

Step 4. Square both values

This means squaring the distance on the x-axis (x₂ - x₁) squared and, separately, squaring the distance on the y-axis (and₂ - and₁).

• 62 = 36 { displaystyle 6 ^ {2} = 36}

• 42=16{displaystyle 4^{2}=16}

Step 5. Add the values you got

This number will give you the square of the diagonal, which is the linear distance between the two points. Continuing with the example of the points (3, 2) and (7, 8), the square of (7 - 3) is 36 and the square of (8 - 2) is 16. 36 + 16 = 52.

Step 6. Find the square root of the number you got

This is the final step to finish solving the equation. The linear distance between two points is the square root of the sum of the square values of distance on the x-axis and on the y-axis.

To end the example: the distance between (3, 2) and (7, 8) is √52 or approximately 7.21 units

Advice

• It doesn't matter if you get a negative number after subtracting y₂ - and₁ or x₂ - x₁. The difference is squared and you will always get a positive distance as the answer.