# A triangle has corners at #(9 ,1 )#, #(2 ,4 )#, and #(5 ,8 )#. How far is the triangle's centroid from the origin?

Add all of the x coordinates of vertices, divide by 3, square that number do the same with the y coordinates add the two together and take the square root.

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To find the centroid of a triangle, you average the coordinates of its vertices.

The coordinates of the centroid are: [ (\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}) ]

Given the coordinates of the vertices: [ (9, 1), (2, 4), (5, 8) ]

The centroid's coordinates are: [ (\frac{9 + 2 + 5}{3}, \frac{1 + 4 + 8}{3}) = (\frac{16}{3}, \frac{13}{3}) ]

The distance from the origin to the centroid is given by the distance formula: [ d = \sqrt{(x - 0)^2 + (y - 0)^2} ]

Substituting the centroid's coordinates: [ d = \sqrt{(\frac{16}{3})^2 + (\frac{13}{3})^2} ]

[ d = \sqrt{\frac{256}{9} + \frac{169}{9}} ]

[ d = \sqrt{\frac{425}{9}} ]

[ d \approx \frac{\sqrt{425}}{3} ]

[ d \approx 7.33 ]

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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 #(8 ,2 )#, #(9 ,7 )#, and #(1 ,4 )#?
- A line passes through #(6 ,4 )# and #(9 ,2 )#. A second line passes through #(3 ,1 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- Which line is perpendicular to the line -2x + 3y = 12 ?
- Circle A has a center at #(2 ,5 )# and a radius of #3 #. Circle B has a center at #(7 ,2 )# and a radius of #3 #. Do the circles overlap? If not, what is the smallest distance between them?
- What is the perimeter of a triangle with corners at #(3 ,4 )#, #(4 ,8 )#, and #(8 ,7 )#?

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