# A triangle has corners at #(1 ,6 )#, #(3 ,2 )#, and #(8 ,9 )#. How far is the triangle's centroid from the origin?

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To find the centroid of a triangle, you can average the x-coordinates of the vertices to find the x-coordinate of the centroid, and similarly average the y-coordinates to find the y-coordinate of the centroid.

Centroid's x-coordinate = (1 + 3 + 8) / 3 = 4 Centroid's y-coordinate = (6 + 2 + 9) / 3 = 5.67 (rounded to two decimal places)

Using the distance formula, we can find the distance between the centroid and the origin:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Distance = sqrt((4 - 0)^2 + (5.67 - 0)^2) Distance = sqrt(16 + 32.16) Distance ≈ sqrt(48.16) Distance ≈ 6.93

So, the distance between the triangle's centroid and the origin is approximately 6.93 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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- A line passes through #(2 ,8 )# and #(4 ,5 )#. A second line passes through #(3 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- Circle A has a center at #(9 ,4 )# and a radius of #3 #. Circle B has a center at #(-1 ,6 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?
- What is the midpoint of the segment whose endpoints are (-1, 4) and (3, 6)?
- A line passes through #(3 ,2 )# and #(7 ,3 )#. A second line passes through #(1 , 4 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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