# A triangle has corners at #(1 ,9 )#, #(5 ,7 )#, and #(3 ,8 )#. How far is the triangle's centroid from the origin?

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Distance of centroid from origin is

Formula to get centroid of a triangle, given the coordinates of three vertices is

Coordinates of centroid

Coordinates of origin

Distance of centroid from origin is

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To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, the distance from the centroid to the origin can be calculated using the distance formula.

Given the coordinates of the vertices: (1, 9), (5, 7), and (3, 8).

The centroid's x-coordinate is the average of 1, 5, and 3, which is (1 + 5 + 3) / 3 = 3. The centroid's y-coordinate is the average of 9, 7, and 8, which is (9 + 7 + 8) / 3 = 8.

So, the centroid of the triangle is at (3, 8).

To find the distance from the centroid to the origin, we use the distance formula:

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

Where (x1, y1) = (0, 0) (coordinates of the origin) and (x2, y2) = (3, 8) (coordinates of the centroid).

So, Distance = sqrt((3 - 0)^2 + (8 - 0)^2) = sqrt(3^2 + 8^2) = sqrt(9 + 64) = sqrt(73).

Therefore, the distance from the centroid to the origin is sqrt(73).

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