How this calculation works
Find where the three altitudes meet using a triangle positioned on the x-axis.
THE FORMULA
With A=(0,0), B=(b,0), C=(x,y), H=(x,x(b−x)/y)A worked example
Vertices (0,0), (6,0), (2,4) give orthocenter (2,2).
Good to know
The third vertex must lie off the x-axis.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Find where the three altitudes meet using a triangle positioned on the x-axis.
The primary result is labeled “Orthocenter x”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The third vertex must lie off the x-axis.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
Vertices (0,0), (6,0), (2,4) give orthocenter (2,2).
Which rule does this calculator apply?
With A=(0,0), B=(b,0), C=(x,y), H=(x,x(b−x)/y)