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

Distance of centroid from origin is

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The centroid of a triangle is the point where the three medians intersect. To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid are ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

Given the coordinates of the vertices as (6, 7), (2, 6), and (5, 2), the centroid can be found by averaging the x-coordinates and y-coordinates:

x-coordinate of centroid = (6 + 2 + 5)/3 = 13/3 y-coordinate of centroid = (7 + 6 + 2)/3 = 15/3

Thus, the centroid of the triangle is at the point (13/3, 5).

The distance between the origin (0,0) and the centroid can be found using the distance formula:

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

Substituting the coordinates of the origin (0,0) and the centroid (13/3, 5), we get:

Distance = √((13/3 - 0)^2 + (5 - 0)^2) = √((13/3)^2 + 5^2) = √(169/9 + 25/1) = √(169/9 + 225/9) = √(394/9)

So, the distance from the origin to the centroid of the triangle is √(394/9).

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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.

- What is the perimeter of a triangle with corners at #(7 ,3 )#, #(9 ,5 )#, and #(3 ,3 )#?
- Circle A has a center at #(3 ,1 )# and a radius of #1 #. Circle B has a center at #(-2 ,1 )# and a radius of #3 #. Do the circles overlap? If not, what is the smallest distance between them?
- Circle A has a center at #(5 ,7 )# and an area of #56 pi#. Circle B has a center at #(9 ,2 )# and an area of #44 pi#. Do the circles overlap?
- Find the equation of the plane passing through (2,3,-1) and perpendicular to the line joining the points (3,4,-1) and (2,-1,5) ?
- What is distance between lines #x+2y=5# and #2x+4y=7#?

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