# What is the orthocenter of a triangle with corners at #(2 ,7 )#, #(1 ,1 )#, and (3 ,2 )#?

Please read the explanation.

The altitude of a triangle is a perpendicular line segment from the vertex of the triangle to the opposite side.

The Orthocenter of a triangle is the intersection of the three altitudes of a triangle.

Construct the triangle

Vertices

Observe that

This angle is greater than

If the triangle is an obtuse triangle, the Orthocenter lies outside the triangle.

Construct altitudes through the vertices of the triangle as shown below:

All the three altitudes meet at a point referred to as the Orthocenter.

Since the triangle is obtuse, the orthocenter lies outside the triangle.

Observe that the Orthocenter has

Hope it helps.

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To find the orthocenter of a triangle, you need to find the point where the altitudes of the triangle intersect. The altitudes are perpendicular lines drawn from each vertex of the triangle to the opposite side.

Given the coordinates of the triangle's vertices: A(2, 7), B(1, 1), and C(3, 2),

First, find the slopes of the lines containing each side of the triangle. Then, use the perpendicular slope relationship to find the slopes of the altitudes. Next, find the equations of the lines containing the altitudes. Finally, solve the system of equations to find the point of intersection, which is the orthocenter.

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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.

- A line segment is bisected by a line with the equation # - 6 y + x = 3 #. If one end of the line segment is at #( 4 , 5 )#, where is the other end?
- A line segment is bisected by a line with the equation # 3 y - 7 x = 2 #. If one end of the line segment is at #(7 ,3 )#, where is the other end?
- What is the orthocenter of a triangle with corners at #(4 ,5 )#, #(3 ,7 )#, and (1 ,6 )#?
- In an Isoceles #triangle# #ABC#,bisector #CD# of the #angle# #C# is equal to the base #BC#.Then the angle between #CDA# is ?
- A triangle has corners A, B, and C located at #(1 ,3 )#, #(3 ,5 )#, and #(4 , 2 )#, respectively. What are the endpoints and length of the altitude going through corner C?

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