The orthocenter is found by intersecting two altitudes. Each altitude is perpendicular to the opposite side.

((x - xA), (y - yA)) · (BC) = 0

Using two such equations avoids slope failures on vertical or horizontal sides.

Enter the coordinates of the triangle’s three vertices. The calculator rejects collinear points before solving the altitude intersection.

1. Enter three points.
2. Make sure they form a triangle.
3. Read the orthocenter coordinates from the result card.

For points (0,0), (4,0), and (0,3), the orthocenter is (0,0).

That is the right-angle vertex of the triangle.

The new solver uses line equations instead of slopes, so vertical sides no longer produce divide-by-zero failures.

Blank and malformed coordinates are rejected before any geometry is performed.