1. What is the Orthocenter?

The orthocenter is the point where the three altitudes of a triangle intersect. An altitude is a perpendicular line segment from a vertex to the opposite side (or its extension).

2. How Does the Calculator Work?

The calculator finds the orthocenter by:

Mathematical Process:

• Find slope of one side
• Calculate perpendicular slope for altitude
• Find equation of altitude line
• Repeat for another side
• Solve system of equations to find intersection

3. Importance of Orthocenter

Details: The orthocenter is one of the triangle's centers of significance in geometry, along with centroid, circumcenter, and incenter. Its position varies depending on the type of triangle.

4. Using the Calculator

Tips: Enter the coordinates of three points that form a triangle. The calculator will determine the orthocenter coordinates.

5. Frequently Asked Questions (FAQ)

Q1: Where is the orthocenter located in different triangles?
A: In acute triangles: inside; right triangles: at right angle vertex; obtuse triangles: outside.

Q2: Does every triangle have an orthocenter?
A: Yes, all triangles have an orthocenter, though it may lie outside the triangle.

Q3: How is orthocenter different from centroid?
A: Centroid is where medians intersect (always inside), while orthocenter is where altitudes intersect.

Q4: What units does the calculator use?
A: The calculator uses the same units as your input coordinates (no unit conversion).

Q5: Can I use this for 3D coordinates?
A: No, this calculator is for 2D coordinates only.