# A triangle has corners at #(2 ,9 )#, #(4 ,2 )#, and #(5 ,1 )#. How far is the triangle's centroid from the origin?

THe distance of the centroid from the origin is

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To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), you use the formula:

Centroid = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

For the given triangle with vertices (2, 9), (4, 2), and (5, 1), the centroid is ((2 + 4 + 5)/3, (9 + 2 + 1)/3) = (11/3, 4).

To find the distance between the centroid and the origin, you use the distance formula:

Distance = √((x - x0)^2 + (y - y0)^2),

where (x0, y0) is the origin (0, 0).

Distance = √((11/3 - 0)^2 + (4 - 0)^2) = √((121/9) + 16) = √((121/9) + (144/9)) = √(265/9) ≈ 5.75.

Therefore, the distance between the centroid of the triangle and the origin is approximately 5.75 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 at #(1 ,5 )#, #(9 ,4 )#, and #(6 ,7 )#. How far is the triangle's centroid from the origin?
- Circle A has a center at #(-4 ,2 )# and a radius of #3 #. Circle B has a center at #(1 ,9 )# and a radius of #2 #. Do the circles overlap? If not what is the smallest distance between them?
- Circle A has a center at #(9 ,8 )# and a radius of #2 #. Circle B has a center at #(-8 ,3 )# and a radius of #1 #. Do the circles overlap? If not, what is the smallest distance between them?
- What is the perimeter of a triangle with corners at #(7 ,3 )#, #(8 ,5 )#, and #(3 ,9 )#?
- Circle A has a center at #(3 ,7 )# and a radius of #1 #. Circle B has a center at #(-3 ,3 )# and a radius of #2 #. Do the circles overlap? If not, what is the smallest distance between them?

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