A triangle has corners at #(5 ,1 )#, #(7 ,2 )#, and #(6 ,3 )#. How far is the triangle's centroid from the origin?

Answer 1

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).

X coordinate of centroid #Gx) = (x_1 + x_2 + x_3) / 3# & Y coordinate of centroid #G(y) = (y_1 + y_2 + y_3) / 3#
#G(x) = (5 + 7 + 6) / 3 = 6#
#G(y) = (1 + 2 + 3) / 3 = 2#
Distance ‘ D’ of centroid ‘G’ from origin is given by #D = sqrt((G(x) - 0)^2 + (G(y) - 0)^2)#
#D = sqrt(G(x)^2 + G(y)^2) = sqrt(6^2 + 2^2) = sqrt (40) = 6.3246#
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Answer 2

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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Answer from HIX Tutor

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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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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