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

From the diagram:

We need to find the endpoints of the altitude passing through

Using point

Using point slope form of a line and point

We now need the equation of the line through point

If two line are perpendicular the the product of their gradients is

Let the unknown gradient be

Using this and point

We solve now solve

Substitute in

So the end points of the altitude are:

The length of the altitude line

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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 ,5 )#, #(3 ,6 )#, and #(8 ,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 #(7 ,6 )#, #(9 ,3 )#, and #(2 ,1 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- Let A be #(−3,5)# and B be #(5,−10))#. Find: (1) the length of segment #bar(AB)# (2) the midpoint #P# of #bar(AB)# (3) the point #Q# which splits #bar(AB)# in the ratio #2:5#?
- A line segment is bisected by a line with the equation # 9 y - 2 x = 5 #. 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 #(3 ,1 )#, #(4 ,5 )#, and (2 ,7 )#?

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