A triangle has corners at #(1 ,1 )#, #(8 ,2 )#, and #(5 ,9 )#. How far is the triangle's centroid from the origin?

Answer 1

The distance #=6.2#

If the corners of a triangle are #(x_1,y_1), (x_2,y_2) and (x_3,y_3)#

Then, the coordinates of the centroid are

#x_c=(x_1+x_2+x_3)/3=(1+8+5)/3=14/3#
#y_c=(y_1+y_2+y_3)/3=(1+2+9)/3=12/3=4#

The distance of the centroid from the origin is

#=sqrt(x_c^2+y_c^2)=sqrt(14^2/9+16)=(sqrt340)/3=6.2#
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Answer 2

To find the distance from the centroid of the triangle to the origin, you can use the formula:

[ D = \sqrt{x^2 + y^2} ]

where ( x ) and ( y ) are the coordinates of the centroid. The coordinates of the centroid ( (x, y) ) can be calculated by taking the average of the coordinates of the triangle's vertices.

[ x = \frac{x_1 + x_2 + x_3}{3} ] [ y = \frac{y_1 + y_2 + y_3}{3} ]

Then, substitute the values of ( x ) and ( y ) into the distance formula to find the distance from the centroid to the origin.

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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.

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.

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.

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.

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