# What is the orthocenter of a triangle with corners at #(4 ,9 )#, #(3 ,7 )#, and (1 ,1 )#?

Orthocenter of the triangle is at

Orthocenter is the point where the three "altitudes" of a triangle meet. An "altitude" is a line that goes through a vertex (corner point) and is at right angles to the opposite side.

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To find the orthocenter of a triangle with vertices at (4, 9), (3, 7), and (1, 1), follow these steps:

- Calculate the slopes of the lines passing through each pair of vertices to find the perpendicular bisectors.
- Find the equations of the perpendicular bisectors.
- Find the intersection point of any two perpendicular bisectors. This point will be the orthocenter of the triangle.

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- Prove the diagonals of a parallelogram bisect each other, i.e. #bar(AE) = bar(EC)# and #bar(BE) = bar(ED)# ?
- What is the orthocenter of a triangle with corners at #(4 ,9 )#, #(3 ,4 )#, and (5 ,1 )#?
- A line segment is bisected by a line with the equation # - 3 y + 6 x = 6 #. If one end of the line segment is at #( 3 , 3 )#, where is the other end?
- A line segment is bisected by a line with the equation # -6 y + 3 x = 2 #. If one end of the line segment is at #( 5 , 1 )#, where is the other end?
- What is the orthocenter of a triangle with corners at #(6 ,2 )#, #(3 ,7 )#, and (4 ,9 )#?

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