Question

(3,-1) and (-2,3) are two vertices of a triangle. Orthocentre of a triangle lie at tha origin .Find third vertices.

Answer 1

Answer:

The orthocenter is the intersecting point for all the altitudes of the triangle. The point where the altitudes of a triangle meet is known as the Orthocenter. In the below mentioned diagram orthocenter is denoted by the letter ‘O’. There is no direct formula to calculate the orthocenter of the triangle. It lies inside for an acute and outside for an obtuse triangle.

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. Vertex is a point where two line segments meet ( A, B and C ).

Orthocenter of a TriangleTo Calculate the slope of the sides of the triangle.

To calculate the perpendicular slope of the sides of the triangle. It gives us the slope of the altitudes of the triangle.

To calculate the equation for the altitudes with their respective coordinates. The point slope formula is given as,

y−y1=m(x−x1)

Finally by solving any two altitude equation, we can get the ortho centre