What is the centroid of a triangle with corners at #(5 , 1 )#, #(0 , 5 )#, and #(3 , 2 )#?

Answer 1

#(8/3,8/3)#

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"=((5+0+3)/3,(1+5+2)/3)=(8/3,8/3)#

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Answer 2

Violet Aldrich

To find the centroid of a triangle with vertices at (5, 1), (0, 5), and (3, 2), you can use the following formula:

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

Substitute the coordinates of the vertices into the formula:

[ \text{Centroid} = \left( \frac{5 + 0 + 3}{3}, \frac{1 + 5 + 2}{3} \right) ]

[ = \left( \frac{8}{3}, \frac{8}{3} \right) ]

So, the centroid of the triangle is located at (\left( \frac{8}{3}, \frac{8}{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.