1. What Is the Orthocenter?

The orthocenter is the intersection point of the three altitudes of a triangle. An altitude is a perpendicular line segment from a vertex to the line containing the opposite side.

2. How the Calculator Works

The calculator finds the orthocenter by:

1. Calculating the slope of two sides of the triangle
2. Determining the equations of the corresponding altitudes (perpendicular to those sides)
3. Finding the intersection point of these two altitudes

3. Importance of Orthocenter

Details: The orthocenter is one of the four main triangle centers (along with centroid, circumcenter, and incenter). Its position reveals properties about the triangle's type:

• Acute triangle: Orthocenter lies inside the triangle
• Right triangle: Orthocenter is at the vertex of the right angle
• Obtuse triangle: Orthocenter lies outside the triangle

4. Using the Calculator

Tips: Enter the coordinates of three non-collinear points. The calculator will determine the orthocenter coordinates.

5. Frequently Asked Questions (FAQ)

Q1: Can the orthocenter be outside the triangle?
A: Yes, in obtuse triangles the orthocenter lies outside the triangle.

Q2: What happens if the points are colinear?
A: The calculator will return "Undefined" as three colinear points don't form a triangle.

Q3: How is the orthocenter different from the centroid?
A: The centroid is the intersection of medians (always inside the triangle), while the orthocenter is the intersection of altitudes.

Q4: Does every triangle have an orthocenter?
A: Yes, every non-degenerate triangle has an orthocenter.

Q5: What's special about the orthocenter in an equilateral triangle?
A: In an equilateral triangle, the orthocenter coincides with the centroid and circumcenter.