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

The distance

Then, the coordinates of the centroid are

The distance of the centroid from the origin is

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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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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 #(7 ,-5 )# and a radius of #1 #. Circle B has a center at #(4 ,2 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?
- A line passes through #(5 ,8 )# and #(6 ,2 )#. A second line passes through #(1 ,3 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(7 ,1 )# to #(8 ,5 )# and the triangle's area is #32 #, what are the possible coordinates of the triangle's third corner?
- A line passes through #(4 ,9 )# and #(7 ,4 )#. A second line passes through #(8 ,7 )#. 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 #(1 ,-4 )# and a radius of #2 #. Circle B has a center at #(9 ,3 )# and a radius of #5 #. Do the circles overlap? If not what is the smallest distance between them?

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