How to Find the Distance Between Two Points

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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:

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{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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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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