Question

Find orthocenter of a triangle formula when the equation is given

Answer 1

Orthocenter of a triangle is the point of intersection of all the altitudes of the triangle. The orthocenter of a triangle is denoted by the letter 'O'. There is no direct formula to calculate the orthocenter of the triangle. The orthocenter of a triangle can be calculated using the following steps:



Step 1: Calculate the slope of the sides of the triangle. The formula to calculate the slope is given as,



Step 2: Calculate the perpendicular slope of the sides of the triangle. It gives us the slope of the altitudes of the triangle. The formula to calculate the perpendicular slope is given as,



Step 3: Then by using point slope form, calculate the equation for the altitudes with their respective coordinates. The point slope formula is given as,



Step 4: Finally by solving any two altitude equation, we can get the orthocenter of the triangle.