# A triangle has corners at #(4 ,4 )#, #(8 ,6 )#, and #(7 ,1 )#. How far is the triangle's centroid from the origin?

8.945(approx)

By signing up, you agree to our Terms of Service and Privacy Policy

To find the centroid of the triangle, you first calculate the average of the x-coordinates and the average of the y-coordinates of the vertices. Then, you use these averages as the coordinates of the centroid.

Given the vertices are (4, 4), (8, 6), and (7, 1), you can find the centroid by averaging the x-coordinates and the y-coordinates:

Average of x-coordinates = (\frac{4 + 8 + 7}{3} = \frac{19}{3})

Average of y-coordinates = (\frac{4 + 6 + 1}{3} = \frac{11}{3})

So, the centroid has coordinates (\left(\frac{19}{3}, \frac{11}{3}\right)).

To find the distance between the centroid and the origin, you can use the distance formula:

Distance = (\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2})

Where ((x_1, y_1)) are the coordinates of the origin (0, 0), and ((x_2, y_2)) are the coordinates of the centroid.

Substituting the values, you get:

Distance = (\sqrt{\left(\frac{19}{3} - 0\right)^2 + \left(\frac{11}{3} - 0\right)^2})

Calculating this expression will give you the distance from the origin to the centroid of the triangle.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- A triangle has corners at #(5 ,2 )#, #(4 ,6 )#, and #(3 ,5 )#. How far is the triangle's centroid from the origin?
- A triangle has corners at #(2 ,9 )#, #(4 ,8 )#, and #(4 ,3 )#. How far is the triangle's centroid from the origin?
- How does one derive the Midpoint Formula?
- Circle A has a center at #(-2 ,-1 )# and a radius of #3 #. Circle B has a center at #(1 ,3 )# 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 #6 #. Circle B has a center at #(-4 ,-8 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7