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

Answer 1

#(4,7/3)#

The #x#-coordinate of the centroid is simply the average of the #x#-coordinates of the triangle's vertices. The same logic is applied to the #y#-coordinates for the #y#-coordinate of the centroid.

#"centroid"=((4+6+2)/3,(4+2+1)/3)=(12/3,7/3)=(4,7/3)#

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Answer 2

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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Answer from HIX Tutor

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.

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.

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