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What is the centroid of a triangle with corners at #(9 , 5 )#, #(6 , 0 )#, and #(2 , 3 )#?

Answer 1

Violet Aldrich

The centroid is located at #(17/3,8/3)#.

The intersection of the medians determines a triangle's centroid, which can be found using the following formula:

#((x_1+x_2+x_3)/3, (y_1+y_2+y_3)/3)#

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

In this example, the vertices are #(9,5), (6,0), (2,3)#

The centroid is

#((9+6+2)/3, (5+0+3)/3)= (17/3, 8/3)#

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Answer 2

Avery Allen

To find the centroid of a triangle with vertices at (9, 5), (6, 0), and (2, 3), you can use the formula for the centroid of a triangle, which is the average of the coordinates of its vertices.

Let the vertices be A(9, 5), B(6, 0), and C(2, 3).

The centroid G is calculated as follows: [ G_x = \frac{x_1 + x_2 + x_3}{3} ] [ G_y = \frac{y_1 + y_2 + y_3}{3} ]

Substitute the coordinates of the vertices into these formulas: [ G_x = \frac{9 + 6 + 2}{3} = \frac{17}{3} ] [ G_y = \frac{5 + 0 + 3}{3} = \frac{8}{3} ]

So, the coordinates of the centroid G are ( \left(\frac{17}{3}, \frac{8}{3}\right) ).

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