# What is the centroid of a triangle with corners at #(4,4 )#, #(6,2 )#, and #(2 , 1 )#?

The

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To find the centroid of a triangle, we can use the formula:

[ \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) ]

where ( (x_1, y_1), (x_2, y_2), ) and ( (x_3, y_3) ) are the coordinates of the triangle's vertices.

Given the coordinates of the triangle's vertices as ( (4, 4), (6, 2), ) and ( (2, 1) ), we can substitute these values into the formula to find the centroid:

[ x_{\text{centroid}} = \frac{4 + 6 + 2}{3} = \frac{12}{3} = 4 ] [ y_{\text{centroid}} = \frac{4 + 2 + 1}{3} = \frac{7}{3} ]

So, the centroid of the triangle is at ( (4, \frac{7}{3}) ).

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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.

- A line segment is bisected by a line with the equation # - 2 y - x = 1 #. If one end of the line segment is at #( 8 , 3 )#, where is the other end?
- A triangle has corners A, B, and C located at #(2 ,7 )#, #(3 ,5 )#, and #(9 , 4 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- What is the centroid of a triangle with corners at #(9 , 5 )#, #(6 , 0 )#, and #(2 , 3 )#?
- A line segment is bisected by line with the equation # 3 y - 3 x = 1 #. If one end of the line segment is at #(2 ,5 )#, where is the other end?
- A triangle has corners A, B, and C located at #(7 ,3 )#, #(4 ,8 )#, and #(3 , 7 )#, respectively. What are the endpoints and length of the altitude going through corner C?

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