# What is the orthocenter of a triangle with corners at #(4 ,1 )#, #(6 ,2 )#, and (3 ,6 )#?

Coordinates of Orthocenter

Orthocenter is the concurring point of the three altitudes of a triangle and represented by ‘O’

Slope of BC

Equation of AD is

Slope of AB

Slope of CF = -(1/m_c) = -2#

Equation of CF is

Solving Eqns (1), (2)

we get the coordinates of Orthocenter

Verification

Slope

Slope of BE = -(1/m_c) = 1/5#

Equation of altitude BE is

Solving equations (2) , (3),

Coordinates of

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To find the orthocenter of a triangle with vertices at (4, 1), (6, 2), and (3, 6), follow these steps:

- Determine the slopes of the lines passing through each pair of vertices.
- Calculate the slopes of the perpendicular bisectors of each side of the triangle.
- Find the point of intersection of these perpendicular bisectors.
- This point is the orthocenter of the triangle.

Performing these calculations will give you the coordinates of the orthocenter.

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