What is the Orthocenter?
Orthocenter Calculator: The orthocenter of a triangle is the point where the three altitudes of the triangle intersect. An altitude of a triangle is a perpendicular line from a vertex to the opposite side (or its extension). The orthocenter can be inside, on, or outside the triangle depending on the type of triangle.
Calculate Orthocenter
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How to Use the Orthocenter Calculator?
To calculate the orthocenter of a triangle, enter the coordinates of the three vertices (A, B, and C). After entering the values, click on the "Calculate" button to get the orthocenter's coordinates. The calculator uses the slope method to find the altitude's intersection point, which is the orthocenter of the triangle.
Formula of Orthocenter Calculation:
To find the orthocenter of a triangle with vertices A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃), use the following method:
1. Calculate the slope of side AB: slope = (y₂ - y₁) / (x₂ - x₁).
2. Find the perpendicular slope to AB: perpendicular slope = -1 / slope.
3. Use the point-slope form to write the equation of the altitude from vertex C.
4. Repeat the process for the other two altitudes and solve the system of equations to find the orthocenter.
FAQ 1: What is an orthocenter?
The orthocenter is the point where the three altitudes of a triangle meet. It can lie inside, outside, or on the triangle depending on the triangle type. The altitudes are perpendiculars from the triangle's vertices to the opposite sides.
FAQ 2: How do you calculate the orthocenter of a triangle?
To calculate the orthocenter, find the equations of the altitudes using the slope of the triangle's sides and then solve the system of linear equations. The intersection of these altitudes is the orthocenter.
FAQ 3: What is an altitude in a triangle?
An altitude in a triangle is a line segment from a vertex perpendicular to the opposite side (or its extension). Every triangle has three altitudes, and they intersect at the orthocenter.
FAQ 4: Can the orthocenter be outside the triangle?
Yes, in the case of an obtuse triangle, the orthocenter lies outside the triangle. For acute triangles, the orthocenter lies inside, and for right triangles, it lies on the right-angled vertex.
FAQ 5: Is the orthocenter always unique?
Yes, for any non-degenerate triangle, the orthocenter is unique. It is always a single point, regardless of the triangle's shape or size.