A triangle has corners at #(2 ,9 )#, #(4 ,8 )#, and #(5 ,3 )#. How far is the triangle's centroid from the origin?

Answer 1

Distance from centroid #=7.6" "#units

Solve the centroid #C(x_c, y_c)# first
#x_c=(x_1+x_2+x_3)/3=(2+4+5)/3=11/3# #y_c=(y_1+y_2+y_3)/3=(9+8+3)/3=20/3#
Solve distance #d# from the origin using #(x_c, y_c)# and #(0, 0)#
#d=sqrt((x_c-0)^2+(y_c-0)^2)#
#d=sqrt((11/3-0)^2+(20/3-0)^2)#
#d=7.608474807" "#units
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Answer 2

The centroid of a triangle is the average of its vertices. The centroid's coordinates are given by the average of the coordinates of the vertices.

The centroid's ( x )-coordinate is ( \frac{2 + 4 + 5}{3} = \frac{11}{3} ). The centroid's ( y )-coordinate is ( \frac{9 + 8 + 3}{3} = \frac{20}{3} ).

Using these coordinates, we can calculate the distance between the centroid and the origin using the distance formula:

[ \text{Distance} = \sqrt{\left(\frac{11}{3}\right)^2 + \left(\frac{20}{3}\right)^2} = \frac{1}{3}\sqrt{401} ].

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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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