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

≈ 5.83 units

The first step here is to calculate the coordinates of the centroid.

Using the 3 vertices given here.

Hence coordinates of centroid = (3 ,5)

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To find the centroid of a triangle, you can average the coordinates of its vertices. Given the vertices at (6, 7), (2, 6), and (1, 2), the centroid is located at the average of these coordinates, which is ((6 + 2 + 1) / 3, (7 + 6 + 2) / 3). Calculating this, we get the centroid at ((9) / 3, (15) / 3), which simplifies to (3, 5).

The distance from the origin to the centroid can be found using the distance formula, which is the square root of the sum of the squares of the coordinates. For the centroid at (3, 5) and the origin at (0, 0), the distance is √(3² + 5²), which simplifies to √(9 + 25), or √34. Thus, the distance from the centroid to the origin is √34.

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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 #(3 ,7 )# and a radius of #2 #. Circle B has a center at #(4 ,-2 )# and a radius of #6 #. Do the circles overlap? If not, what is the smallest distance between them?
- What is the perimeter of a triangle with corners at #(3 ,3 )#, #(1 ,5 )#, and #(2 ,1 )#?
- Circle A has a center at #(2 ,3 )# and an area of #8 pi#. Circle B has a center at #(13 ,7 )# and an area of #54 pi#. Do the circles overlap?
- A line passes through #(9 ,2 )# and #( 3, 5 )#. A second line passes through #( 4, 8 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- What is the perimeter of a triangle with corners at #(7 ,3 )#, #(1 ,5 )#, and #(2 ,4 )#?

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