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What is the centroid of a triangle with corners at #(1 , 3 )#, #(6 , 9 )#, and #(2 , 7 )#?

Answer 1

Caroline Aucoin

The centroid is

#= 3 , (19)/3#

The coordinates provided are #(1,3) = color(blue)(x_1,y_1# #(6,9) = color(blue)(x_2,y_2# #(2,7) = color(blue)(x_3,y_3#

The following formula is needed to determine the centroid:

centroid #=color(blue)[ (x_1+x_2+x_3)/3 , (y_1+y_2+y_3)/3]#

#= (1+6+2)/3 , (3 +9+7)/3#

#= (9)/3 , (19)/3#

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Answer 2

Sadie Adams

To find the centroid of a triangle with vertices at coordinates ( (x_1, y_1) ), ( (x_2, y_2) ), and ( (x_3, y_3) ), use the formula:

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

Substitute the given coordinates into this formula:

[ \left( \frac{1 + 6 + 2}{3}, \frac{3 + 9 + 7}{3} \right) ]

Simplify the expressions:

[ \left( \frac{9}{3}, \frac{19}{3} \right) ]

So, the centroid of the triangle is at ( \left( 3, \frac{19}{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.