# A triangle has corners at #(1 ,6 )#, #(7 ,4 )#, and #(5 ,9 )#. How far is the triangle's centroid from the origin?

the centroid is

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To find the centroid of a triangle, you calculate the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, the distance from the centroid to the origin can be found using the distance formula.

First, calculate the centroid:

Average x-coordinate: ((1 + 7 + 5) / 3 = 13/3)

Average y-coordinate: ((6 + 4 + 9) / 3 = 19/3)

So, the centroid is at ((13/3, 19/3)).

Now, find the distance from the centroid to the origin:

[ d = \sqrt{(13/3)^2 + (19/3)^2} ]

[ d = \sqrt{(169/9) + (361/9)} ]

[ d = \sqrt{530/9} ]

[ d = \sqrt{\frac{530}{9}} ]

[ d = \frac{\sqrt{530}}{3} ]

Therefore, the distance from the centroid to the origin is ( \frac{\sqrt{530}}{3} ) 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.

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