# A triangle has corners at #(9 ,3 )#, #(6 ,7 )#, and #(3 ,2 )#. How far is the triangle's centroid from the origin?

Centroid is

To find the centroid you need to find the midpoints using

Midpoint between

Midpoint between

Midpoint between

Connect the midpoints to the angle opposite. The intersection is the centroid:

The centroid is found at

The distance from

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To find the centroid of a triangle, you can calculate the average of the coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin. The formula for the distance between two points (x1, y1) and (x2, y2) is given by:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

After calculating the centroid's coordinates, you can use the distance formula with the coordinates of the centroid and the origin (0, 0) to find the distance.

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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.

- Find the new equation of the curve #(x-2)^2=y(y-1)^2# by transforming to parallel axes through the point #(2, 1)#?
- A line passes through #(3 ,9 )# and #(6 ,8 )#. A second line passes through #(7 ,6 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- A line passes through #(1 ,4 )# and #(7 ,4 )#. A second line passes through #(8 ,1 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- Circle A has a center at #(3 ,-1 )# and a radius of #3 #. Circle B has a center at #(-2 ,-4 )# and a radius of #7 #. Do the circles overlap? If not, what is the smallest distance between them?
- Circle A has a center at #(7 ,5 )# and an area of #78 pi#. Circle B has a center at #(9 ,2 )# and an area of #54 pi#. Do the circles overlap?

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