MATH CALCULATOR
Orthocenter Calculator
Calculate the orthocenter of a triangle using its vertices’ coordinates.
What is the Orthocenter Calculator & How does it work?
The orthocenter of a triangle is the point where all three altitudes intersect. An altitude is a line segment from a vertex perpendicular to the opposite side.The area A can be calculated using the determinant method: (A = frac{1}{2} |x_1(y_2 – y_3) + x_2(y_3 – y_1) + x_3(y_1 – y_2)|).
H_x = frac{x_1 (y_2 – y_3) + x_2 (y_3 – y_1) + x_3 (y_1 – y_2)}{2 (A)}
H_y = frac{y_1 (x_2 – x_3) + y_2 (x_3 – x_1) + y_3 (x_1 – x_2)}{2 (A)}
H_y = frac{y_1 (x_2 – x_3) + y_2 (x_3 – x_1) + y_3 (x_1 – x_2)}{2 (A)}
x = x-coordinate of a vertex
y = y-coordinate of a vertex
A = Area of the triangle
y = y-coordinate of a vertex
A = Area of the triangle
Parameters
Orthocenter—
Frequently Asked Questions
How do I find the orthocenter of a triangle?
To find the orthocenter, use the formula H_x = (x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)) / 2A and H_y = (y1(x2 – x3) + y2(x3 – x1) + y3(x1 – x2)) / 2A, where A is the area of the triangle calculated using the determinant method.
What are altitudes in a triangle?
Altitudes are line segments from each vertex of the triangle perpendicular to the opposite side. The orthocenter is where these three altitudes intersect.
Can this calculator handle any type of triangle?
Yes, this calculator can find the orthocenter for acute, obtuse, and right triangles as long as you provide the correct vertex coordinates.
How do I input the vertices’ coordinates?
Enter the x and y coordinates of each triangle vertex into the respective fields in the calculator.
What is the area A used in the formula?
The area A is calculated using the determinant method: A = 0.5 * |x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)|.
Is there a limit to the size of the triangle?
No, this calculator can handle triangles of various sizes as long as the input coordinates are accurate and within reasonable limits for computation.
Can I use negative numbers for the coordinates?
Yes, you can use negative numbers for the x and y coordinates of the vertices. The calculator will still compute the orthocenter correctly.
Results are for informational purposes only and do not constitute professional advice.