The Orthocenter is the point where the three altitudes of a triangle intersect. An altitude is a perpendicular line drawn from a vertex to the opposite side. The Orthocenter of Triangle Calculator automates the finding of this intersection point using slope and linear equation logic.
Features
Altitude Intersection: Solves for the crossing point of perpendicular drops.
Coordinate Based: Precise (x, y) output based on vertex inputs.
Dynamic Diagram: Shows the triangle and the position of the Orthocenter (H).
Robust Math: Handles vertical/horizontal lines (undefined slopes) gracefully.
How to Use This Calculator
Coordinates: Enter the x,y positions for vertices A, B, and C.
Find H: Click to calculate.
Interpret: See the coordinates of H.
Check Graph: Notice if H is inside (Acute) or outside (Obtuse).
Formulas
The calculator uses the following mathematical principles:
Slope of Side: $$ m_{BC} = \frac{y_3-y_2}{x_3-x_2} $$
Slope of Altitude: $$ m_{alt} = -1 / m_{BC} $$
Point-Slope Form: $$ y – y_1 = m_{alt}(x – x_1) $$
Practical Applications
Triangle Centers: Crucial in Euler Line studies (Centroid, Circumcenter, Orthocenter are collinear).
Structural Design: Analyzing stress lines perpendicular to supports.
Graphics: Algorithms involving heights of polygons.
Tips for Success
Right Triangle: The orthocenter is the vertex at the right angle itself.
Obtuse Triangle: The orthocenter lies outside the triangle.
Acute Triangle: The orthocenter lies inside the triangle.
Frequently Asked Questions (FAQ)
What is an altitude?
It is the line segment from a vertex perpendicular to the line containing the opposite side.
Why do I get ‘Undefined’?
This usually means the points are collinear (form a line, not a triangle), so no altitudes exist.
Final Words
Navigate the heights of geometry. The Orthocenter of Triangle Calculator precisely locates the intersection of altitudes, giving you deep insight into the perpendicular structure of your triangle.
