# What is the orthocenter of a triangle with corners at #(1, 3)#, #(6, 2)#, and #(5, 4)#?

Let: A(1, 3), B(6, 2) and C(5, 4) be the vertices of triangle ABC:

To check the answer you can find the equation of altitude from B to AC and find the intersection of that with one of the other altitudes.

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The orthocenter of the triangle with vertices at (1, 3), (6, 2), and (5, 4) is located at the point (4.8, 2.6).

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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. An altitude is a line segment drawn from a vertex perpendicular to the opposite side. To find the altitude, you first find the slope of the line containing the side opposite the vertex and then use the negative reciprocal of that slope to find the slope of the altitude. Next, you use the point-slope form of a line equation to find the equation of the altitude. Then, you find the point of intersection of the three altitudes, 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 triangle has corners A, B, and C located at #(4 ,7 )#, #(3 ,2 )#, and #(2 ,4 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- A line segment is bisected by a line with the equation # -7 y + 5 x = 1 #. If one end of the line segment is at #(1 ,4 )#, where is the other end?
- What is the height of the screen?
- Describe and write an equation for the locus of points equidistant form #A(a_x, a_y) and B(b_x,b_y)#? Test what you derived for #P_A(-2,5) and P_B(6,1)? #
- What is the orthocenter of a triangle with corners at #(9 ,3 )#, #(6 ,9 )#, and (2 ,4 )#?

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