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

See explanation.

Additionally, this line's equation will be since it passes through c.

After utilizing the AB equation to solve this line

Now, we can determine the altitude's length by using the distance formula between this point and C.

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To find the endpoints and length of the altitude going through corner C of the triangle with vertices A(2, 7), B(1, 4), and C(6, 3), follow these steps:

- Find the slope of the line segment AB.
- Use the perpendicular property of the altitude to find the negative reciprocal of the slope of AB. This gives the slope of the line containing the altitude passing through C.
- Use the point-slope form to find the equation of the line containing the altitude passing through C.
- Find the intersection point of the altitude line and the line segment AB. This intersection point is one endpoint of the altitude.
- Repeat steps 1-4 for the line segment AC to find the other endpoint of the altitude.
- Calculate the distance between the two endpoints to find the length of the altitude.

After calculations, the endpoints of the altitude through corner C are:

Endpoint 1: (3.2, 4.8) Endpoint 2: (5.2, 5.6)

The length of the altitude is approximately 1.92 units.

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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 #(5 ,2 )#, #(2 ,5 )#, and #(8 ,7 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- What is the orthocenter of a triangle with corners at #(9 ,7 )#, #(2 ,4 )#, and (8 ,6 )#?
- What is the orthocenter of a triangle with corners at #(3 ,3 )#, #(2 ,4 )#, and (7 ,9 )#?
- A line segment is bisected by a line with the equation # 3 y - 8 x = 2 #. If one end of the line segment is at #(1 ,3 )#, where is the other end?
- A triangle has corners A, B, and C located at #(5 ,5 )#, #(3 ,9 )#, and #(4 , 1 )#, respectively. What are the endpoints and length of the altitude going through corner C?

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