What is the centroid of a triangle with corners at #(5 , 7 )#, #(3 , 5 )#, and #(6 , 2 )#?

Answer 1

Sophia Alfred

The centroid #=(14/3 , 14/3)#

The coordinates of the vertices of the triangle are

#(5,7) = color(blue)(x_1,y_1#

#(3,5) = color(blue)(x_2,y_2#

#(6,2) = color(blue)(x_3,y_3#

This formula is used to find the centroid:

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

#=(5+3+6)/3 , (7+5+2)/3#

#=14/3 , 14/3#

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Answer 2

Autumn Armstrong

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)

Using the given coordinates:

(x1, y1) = (5, 7) (x2, y2) = (3, 5) (x3, y3) = (6, 2)

Plug these values into the formula:

Centroid = ((5 + 3 + 6) / 3, (7 + 5 + 2) / 3) = (14 / 3, 14 / 3) = (4.67, 4.67)

So, the centroid of the triangle with corners at (5, 7), (3, 5), and (6, 2) is approximately (4.67, 4.67).

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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.