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

Hence, the orthocentre of

Let ,

We take,

So,

It is clear that,

Hence,

Hence, the orthocentre of

Please see the graph:

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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 altitude is a line segment from one vertex perpendicular to the opposite side.

Step 1: Find the slopes of the lines passing through each side of the triangle. Step 2: Find the equations of the perpendicular lines passing through each vertex. Step 3: Find the intersection point of these lines, which will be 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.

- In a #DeltaABC#, right angled at #A#, a point #D# is on side #AB#. Prove that #CD^2=BC^2+BD^2#?
- What is the orthocenter of a triangle with corners at #(1, 3)#, #(6, 2)#, and #(5, 4)#?
- What is the centroid of a triangle with vertices at #(a, b)#, #(c, d)#, and #(e, f)#?
- A triangle has corners A, B, and C located at #(6 ,8 )#, #(7 ,4 )#, and #(5 ,3 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- A triangle has corners at #(5 , 4 )#, ( 7 , 9)#, and #( 5 , 8 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?

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