Similarly, we have to find the equation of the lines BE and CF.Įquation for the line BE with points (0,5) and slope -1/9 = y-5 = -1/9(x-0)īy solving the above, we get the equation x + 9y = 45 -2Įquation for the line CF with points (3,-6) and slope 2 = y+6 = 2(x-3)īy solving the above, we get the equation 2x - y = 12 -3įind the values of x and y by solving any 2 of the above 3 equations. Lets find the equation of the line AD with points (4,3) and the slope 3/11.įormula to find the equation of orthocenter of triangle = y-y1 = m(x-x1)īy solving the above, we get the equation 3x-11y = -21 -1 Once we find the slope of the perpendicular lines, we have to find the equation of the lines AD, BE and CF. The slope of the altitude = -1/slope of the opposite side in triangle. Now, lets calculate the slope of the altitudes AD, BE and CF which are perpendicular to BC, CA and AB respectively. Kindly note that the slope is represented by the letter 'm'. Lets find with the points A(4,3), B(0,5) and C(3,-6).įind the slope of the sides AB, BC and CA using the formula y2-y1/x2-x1.Ĭonsider the points of the sides to be x1,y1 and x2,y2 respectively. Orthocenter of Triangle Method to calculate the orthocenter of a triangle In the below example, o is the Orthocenter. Vertex is a point where two line segments meet ( A, B and C ). Altitudes are nothing but the perpendicular line ( AD, BE and CF ) from one side of the triangle ( either AB or BC or CA ) to the opposite vertex. Notably, the three altitudes of a triangle are concurrent. Altitude can also be used to refer to the specific length of this segment. It is the shortest line segment between a vertex of a triangle and the (possibly extended) opposite side. It lies inside for an acute and outside for an obtuse triangle. The altitude or height of a triangle is the distance between a vertex of a triangle and the opposite side. The point where the altitudes of a triangle meet is known as the Orthocenter.

Definition of an altitude geometry