# A triangle has corners at #(7 ,2 )#, #(6 ,7 )#, and #(3 ,1 )#. How far is the triangle's centroid from the origin?

The distance is

The centroid is

Therefore,

The distance from the origin is

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The centroid of a triangle can be found by taking the average of the coordinates of its vertices. In this case, the centroid is located at ((7+6+3)/3, (2+7+1)/3). Calculate the distance between this centroid and the origin using the distance formula, which is the square root of the sum of the squares of the coordinates.

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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.

- Circle A has a center at #(-4 ,2 )# and a radius of #3 #. Circle B has a center at #(2 ,-1 )# and a radius of #3 #. Do the circles overlap? If not what is the smallest distance between them?
- An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(4 ,9 )# to #(8 ,5 )# and the triangle's area is #48 #, what are the possible coordinates of the triangle's third corner?
- Circle A has a center at #(4 ,-1 )# and a radius of #3 #. Circle B has a center at #(-3 ,6 )# and a radius of #2 #. Do the circles overlap? If not, what is the smallest distance between them?
- Circle A has a center at #(5 ,-2 )# and a radius of #2 #. Circle B has a center at #(4 ,6 )# and a radius of #3 #. Do the circles overlap? If not what is the smallest distance between them?
- What is the slope-intercept form of the equation of the line through the point (-8, 7) and parallel to the line: #x + y = 13#?

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