Calculate distance between two points
Calculating the distance between two points in the coordinate system
On this page the distance between two points in the coordinate system is calculated. To do this, enter the X / Y coordinates of the two points A and B. It doesn't matter which point is first and which is second. The result will be the same.
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Formula for distance between two points
To find the distance between two points, use the distance formula. In the formula, x and y stand for the position on a coordinate plane.
\(d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)
In the graphic above, the two elements a and b form the legs of a right triangle. The following Pythagorean theorem can therefore be used to calculate the distance c.
\( \displaystyle c=\sqrt{a^2 + b^2}\)
The values for a and b are calculated from the distance between the x and y coordinates
Distance of the Y coordinates
\(\displaystyle a=y_2-y_1\)
Distance of the X coordinates
\(\displaystyle b= x_2-x_1\)
If that is summed up in one formula, the distance formula above results for calculating the distance between the points.
Calculate the angle to the X axis
\(\displaystyle α=asin\left(\frac{a}{c}\right) \) \(\displaystyle = asin\left(\frac{y_2-y_1}{\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}}\right)\)
\(\displaystyle α=acos\left(\frac{b}{c}\right) \) \(\displaystyle = acos\left(\frac{x_2-x_1}{\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}}\right)\)
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