# A triangle has corners at #(5 ,6 )#, #(3 ,7 )#, and #(8 ,9 )#. How far is the triangle's centroid from the origin?

The answer is

Therefore,

The distance from the origin is

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The centroid of a triangle is located at the average of its vertices' coordinates. So, to find the centroid, calculate the average of the x-coordinates and the average of the y-coordinates of the vertices. Then, use the distance formula to find the distance between the centroid and the origin, which is (0, 0).

Centroid coordinates: x-coordinate = (5 + 3 + 8) / 3 = 16 / 3 y-coordinate = (6 + 7 + 9) / 3 = 22 / 3

Distance from the origin: √((16/3)^2 + (22/3)^2) ≈ 7.72 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.

- Find the equation of the enveloping cylinder of the sphere #x^2+y^2+z^2-2x+4y=1# with its lines parallel to #x/2=y/3,z=0#?
- Circle A has a center at #(5 ,3 )# and an area of #4 pi#. Circle B has a center at #(2 ,8 )# and an area of #16 pi#. Do the circles overlap? If not, what is the shortest distance between them?
- A triangle has corners at #(5 ,2 )#, #(2 ,7 )#, and #(3 ,5 )#. How far is the triangle's centroid from the origin?
- Circle A has a center at #(5 ,8 )# and an area of #18 pi#. Circle B has a center at #(3 ,1 )# and an area of #27 pi#. Do the circles overlap?
- The equation of line m is 4x + 5y = -2. What is the slope of a line that is perpendicular to line m?

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