What is the centroid of a triangle with corners at #(3, 2 )#, #(5,5 )#, and #(12 , 9 )#?

Answer 1

The centroid # = (20)/3 , (16)/3#

The corners of the triangle are #(3,2) = color(blue)(x_1,y_1# #(5,5) = color(blue)(x_2,y_2# # (12,9) = color(blue)(x_3,y_3#

The formula is used to find the centroid.

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

# = (3+5+12)/3 , (2+5+9)/3#

# = (20)/3 , (16)/3#

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Answer 2

Aaliyah Anderson

To find the centroid of a triangle with vertices at (3, 2), (5, 5), and (12, 9), you can use the formula:

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

Substituting the coordinates of the vertices:

[ x_1 = 3, \quad x_2 = 5, \quad x_3 = 12 ] [ y_1 = 2, \quad y_2 = 5, \quad y_3 = 9 ]

[ \text{Centroid} = \left( \frac{3 + 5 + 12}{3}, \frac{2 + 5 + 9}{3} \right) ]

[ \text{Centroid} = \left( \frac{20}{3}, \frac{16}{3} \right) ]

So, the centroid of the triangle is at ( \left( \frac{20}{3}, \frac{16}{3} \right) ).

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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.