Euler Line Calculator

This calculator computes the slope of the Euler line. The Euler line passes through important points of a triangle: the centroid (the center of mass), the orthocenter (where the altitudes meet) and the circumcenter (the center of the circumscribed circle) of a triangle. 
Calculation👉Note, the Euler line is a line determined from any triangle that is not equilateral.
Inputs﻿﻿M1
:2​
﻿
﻿﻿M2
:0.75​
﻿
﻿﻿M3
:7​
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﻿
Outputs﻿﻿Me
:-0.576​
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﻿
﻿
Where:
﻿﻿f(x)=M1+M2+M3+3∗M1∗M2∗M3−M1∗M2+M1∗M3+M2∗M3+3​
﻿
﻿﻿M1
 is the first slope of the triangle's side within the cartesian coordinates system, the Rise over run values.
﻿﻿M2
 is the Second slope of the triangle's side within the cartesian coordinates system, the Rise over run values.
﻿﻿M3
 is the Third slope of the triangle's side within the cartesian coordinates system, the Rise over run values.
﻿﻿Me
 is the resulting slope of the Euler line in a cartesian coordinate system. Therefore, this gradient forms the equation of a line for the Euler Line.
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﻿
ExplanationThe Euler line is a special line that can be drawn through a triangle, that passes through three interesting points of a triangle:
Centroid (G), is the intersection point of the medians of the triangle. The median lines are located from each vertex to the midpoint of the opposite side.
Orthocenter (H), is the intersection point of the altitudes of the triangle. The altitude lines are drawn from each vertex and is perpendicular to the opposite side.
Circumcenter (O), is the intersection point of the perpendicular bisectors of the sides, which is also the center of the circumcircle of the triangle.
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Euler line passing through important points of a triangle
👉For right-angle triangles, the Euler Line is always the line that passes through right-angle vertex and hypotenuse midpoint.
Related ResourcesEquilateral Triangle Calculator 
Heron's Formula Calculator 
Tangential Angle Method for setting out circular curves 
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