What is the centroid of a triangle with corners at #(3, 2 )#, #(1,5 )#, and #(0 , 9 )#?

Answer 1

#(4/3,16/3)#

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"=((3+1+0)/3,(2+5+9)/3)=(4/3,16/3)#

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Answer 2

Claire Akin

To find the centroid of a triangle with vertices at (x₁, y₁), (x₂, y₂), and (x₃, y₃), you can use the formula:

Centroid = ((x₁ + x₂ + x₃) / 3, (y₁ + y₂ + y₃) / 3)

Given the vertices: Vertex 1: (3, 2) Vertex 2: (1, 5) Vertex 3: (0, 9)

Using the formula:

Centroid = ((3 + 1 + 0) / 3, (2 + 5 + 9) / 3)

Calculating:

Centroid = ((4 / 3), (16 / 3))

So, the centroid of the triangle is approximately (1.33, 5.33).

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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.