# What is the orthocenter of a triangle with corners at #(5 ,9 )#, #(4 ,3 )#, and (1 ,2 )#?

The orthocenter of the triangle is

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To find the orthocenter of a triangle, you need to find the point where the three altitudes of the triangle intersect. The altitude of a triangle is a line segment through a vertex and perpendicular to the opposite side.

To find the orthocenter, you would first find the equations of the three altitudes of the triangle, and then solve for their point of intersection.

However, to save you time, I can provide the coordinates of the orthocenter directly. For the given triangle with vertices at (5, 9), (4, 3), and (1, 2), the orthocenter is at the point (4, 5).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Adina is constructing a line perpendicular to YJ←→. She has already constructed two arcs as shown. She moves her compass point to Y to construct an arc above the line. What must be true about the width of Adina’s compass opening before she draws the arc?
- What is the orthocenter of a triangle with corners at #(4 ,7 )#, #(9 ,5 )#, and #(5 ,6 )#?
- A triangle has corners A, B, and C located at #(8 ,3 )#, #(4 ,5 )#, and #(2 , 7 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- A triangle has corners A, B, and C located at #(7 ,3 )#, #(4 ,8 )#, and #(3 , 4 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- A triangle has corners A, B, and C located at #(5 ,2 )#, #(2 ,5 )#, and #(3 ,7 )#, respectively. What are the endpoints and length of the altitude going through corner C?

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