Orthocenter Calculator Coordinates Plane

Orthocenter Calculation:

\[ \text{Orthocenter is the intersection point of the three altitudes of a triangle} \]

Point A x-coordinate:

Point A y-coordinate:

Point B x-coordinate:

Point B y-coordinate:

Point C x-coordinate:

Point C y-coordinate:

Orthocenter Coordinates:

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1. What is an 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 Does the Calculator Work?

The calculator finds the orthocenter by:

Calculating slopes of two sides of the triangle
Finding the slopes of the corresponding altitudes (negative reciprocals)
Determining the equations of two altitudes
Solving the system of equations to find their intersection point

3. Importance of Orthocenter Calculation

Details: The orthocenter is an important point of concurrency in triangle geometry, used in various geometric proofs and constructions.

4. Using the Calculator

Tips: Enter the coordinates of three non-colinear 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 the right angle vertex; obtuse triangles: outside.

Q2: Can any three points have an orthocenter?
A: Only if they form a proper triangle (not colinear).

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

Q4: What's special about the orthocenter?
A: In any triangle, the orthocenter, centroid, and circumcenter lie on the Euler line.

Q5: How precise are the calculations?
A: Results are rounded to 2 decimal places for clarity.