A triangle has corners at #(5 ,2 )#, #(9 ,7 )#, and #(6 ,5 )#. How far is the triangle's centroid from the origin?
Distance of Centroid G from origin O is
To find the distance
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To find the centroid of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid are given by the average of the x-coordinates and the average of the y-coordinates:
Centroid's x-coordinate (Cx) = (x1 + x2 + x3) / 3 Centroid's y-coordinate (Cy) = (y1 + y2 + y3) / 3
Using the given coordinates:
x1 = 5, y1 = 2 x2 = 9, y2 = 7 x3 = 6, y3 = 5
Cx = (5 + 9 + 6) / 3 = 20 / 3 ≈ 6.67 Cy = (2 + 7 + 5) / 3 = 14 / 3 ≈ 4.67
Now, to find the distance from the centroid to the origin (0, 0), you can use the distance formula:
Distance = √((Cx - 0)^2 + (Cy - 0)^2)
Plugging in the values:
Distance = √((6.67 - 0)^2 + (4.67 - 0)^2) Distance ≈ √(44.4889 + 21.8089) Distance ≈ √66.2978 Distance ≈ 8.14 (approximately)
So, the distance from the triangle's centroid to the origin is approximately 8.14 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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