# What is the centroid of a triangle with vertices at #(a, b)#, #(c, d)#, and #(e, f)#?

The centroid is the average of the coordinates:

The point where the medians intersect is known as the centroid of a triangle.

The line segments that join each vertex to the opposite side's midpoint are known as medians.

Theorem: A triangle's medians are contemporaneous.

If three medians are concurrent, then they meet at some point.

Proof: Just solve the median equations and find the points where the pairs intersect.

Since parametric forms are simple to write, let's use them.

When do medials 1 and 2 meet?

Two equations there,

This indicates that the centroid is

Naturally, if we had applied the first and third or second and third median equations, we would have obtained the same result.

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The centroid of a triangle with vertices at ((a, b)), ((c, d)), and ((e, f)) is given by the coordinates:

[ \left( \frac{a + c + e}{3}, \frac{b + d + f}{3} \right) ]

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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.

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