A triangle has corners at #(5 ,1 )#, #(7 ,2 )#, and #(6 ,3 )#. How far is the triangle's centroid from the origin?
Centroid is 6.3246 from the origin
Coordinates of Centroid of a triangle is obtained as below : Let G be the centroid and the coordinates G(x), G(y).
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To find the centroid of a triangle, you average the x-coordinates of the vertices to find the x-coordinate of the centroid, and you average the y-coordinates of the vertices to find the y-coordinate of the centroid.
So, the centroid of the triangle with vertices at (5,1), (7,2), and (6,3) is:
x-coordinate of centroid = (5 + 7 + 6) / 3 = 18 / 3 = 6 y-coordinate of centroid = (1 + 2 + 3) / 3 = 6 / 3 = 2
Therefore, the centroid is at (6, 2).
The distance from the origin to the centroid can be found using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) = (0, 0) (the origin) and (x2, y2) = (6, 2) (the centroid).
Distance = √((6 - 0)^2 + (2 - 0)^2) = √(6^2 + 2^2) = √(36 + 4) = √40 ≈ 6.32 units
So, the distance from the origin to the centroid of the triangle is approximately 6.32 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.
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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