Quickly find the orthocenter of any triangle using our free online calculator. Simply input the coordinates of the three vertices, and get instant, accurate results for your geometry calculations. Perfect for students, teachers, and professionals working with geometric figures.
Formula:
The orthocenter (H) of a triangle is the intersection point of its three altitudes. To find H, the calculator first determines the equations of at least two altitudes. For an altitude from vertex A(x1, y1) to side BC, its slope (mAD) is the negative reciprocal of the slope of BC (mBC). The equation of the altitude is then y - y1 = mAD(x - x1). By solving the system of equations for two altitudes, the coordinates (x, y) of the orthocenter are found.