# A triangle has corners A, B, and C located at #(1 ,1 )#, #(6 ,8 )#, and #(7 ,4 )#, respectively. What are the endpoints and length of the altitude going through corner C?

Endpoint:

Height:

Here is a graph.

What we want to know is the endpoint(

[Step1: determine the line

The slope of line

[Step2: determinte the line

If the two lines with slope

Thus, the slope of line CH is

Its equation is

[Step3: calculate the endpoint and height]

Solving the system equations

and the endpoint

The length of CH is calculated below:

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The endpoints of the altitude going through corner C are (7, 4) and the foot of the altitude, which is the point where the altitude intersects the side opposite corner C. To find the foot of the altitude, first, determine the slope of the line passing through points A and B. Then, find the perpendicular slope to this line, which will be the slope of the altitude. Finally, using the slope of the altitude and the coordinates of point C, find the equation of the line passing through C with this slope. Solve this equation along with the equation of the line passing through points A and B to find the foot of the altitude. Once you have the foot of the altitude, you can calculate the length of the altitude using the distance formula between point C and the foot of the altitude.

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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 ,2 )#, #(3 ,4 )#, and #(6 ,8 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- A triangle has corners A, B, and C located at #(8 ,7 )#, #(1 ,5 )#, and #(6 , 3 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- A triangle has corners A, B, and C located at #(1 ,3 )#, #(9 ,5 )#, and #(6 ,2 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- What is the orthocenter of a triangle with corners at #(3 ,1 )#, #(4 ,5 )#, and (2 ,2 )#?
- A triangle has corners A, B, and C located at #(7 ,6 )#, #(8 ,3 )#, and #(2 ,1 )#, respectively. What are the endpoints and length of the altitude going through corner C?

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