How to Find the Distance Between Two Points

You will treat the distance between two points as a line segment. The length of this line segment is calculated using the distance formula: $($ $($ $x$ $2$ $-$ $x$ $first$ $)$ $2$ $+$ $($ $y$ $2$ $-$ $y$ $first$ $)$ $2$ $)$ ${displaystyle {sqrt {(}}(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2})}$ $How to Find the Distance Between Two Points$ .

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Use the coordinates of the two points that you want to find the distance between them. Suppose Point 1 has coordinates (x1,y1) and Point 2 has coordinates (x2,y2). It doesn’t matter which point is which, you just need to keep the names (1 and 2) consistent throughout the problem. ^{[1] X Research Source}

x1 is the horizontal coordinate (along the x-axis) of Point 1, and x2 is the horizontal coordinate of Point 2. y1 is the vertical coordinate (along the y-axis) of Point 1, and y2 is the coordinate in vertical of Point 2.
For example, we will take 2 points with coordinates (3,2) and (7,8). If (3,2) is (x1,y1) then (7,8) is (x2,y2).

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Formula for calculating distance. This formula is used to calculate the length of the line segment connecting two points: Point 1 and Point 2. The distance between two points is the square root of the sum square of the horizontal distance and the square of the vertical distance. between two points. ^{[2] X Research Source} Simply put, it is the square root of:

(

x

2

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x

first

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2

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(

y

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2

{displaystyle (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}

{displaystyle (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}

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Find the horizontal and vertical distance between two points. First, take y2 – y1 to find the vertical distance. Then take x2 – x1 to find the horizontal distance. Don’t worry if subtraction is negative. The next step is to square these values, and squaring always gives a positive result. ^{[3] X Research Sources}

Find the y-axis distance. Take for example points (3,2) and (7,8), where (3,2) is Score 1 and (7,8) is Score 2: (y2 – y1) = 8 – 2 = 6. That is, there are six units of distance on the y-axis between the two points.
Find the distance along the x-axis. For 2 points with coordinates (3,2) and (7,8): (x2 – x1) = 7 – 3 = 4. That is, there are four distance units on the x-axis between the two points.

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Square both values. That is, you will square the x-axis distance (x2 – x1) and square the y-axis distance (y2 – y1).

$6$ $2$ $=$ $36$ ${displaystyle 6^{2}=36}$ ${displaystyle 6^{2}=36}$
$4$ $2$ $=$ $16$ ${displaystyle 4^{2}=16}$ ${displaystyle 4^{2}=16}$

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Add the squared values together. As a result you will have the square of the linear diagonal between the two points. For points (3,2) and (7,8), the square of (7 – 3) is 36, and the square of (8 – 2) is 16. 36 + 16 = 52.

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Calculate the square root of this equation. This is the last step in the equation. The line segment joining the two points is the square root of the sum of the squared values. ^{[4] X Research Sources}

Continuing with the example above: the distance between (3,2) and (7,8) is the square root of (52), approximately 7.21 units.

Advice

Don’t worry if you get negative number after subtracting y2 – y1 or x2 – x1. Since this result will be squared afterwards, and you always get a positive value for the distance. ^{[5] X Research Sources}

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