# A triangle has corners at #(4 ,1 )#, #(6 ,3 )#, and #(3 ,8 )#. How far is the triangle's centroid from the origin?

Distance of centroid from origin is

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

To find the centroid of a triangle, you calculate the average of the x-coordinates and the average of the y-coordinates of its vertices. The formula for the centroid of a triangle is:

[ (\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}) ]

Given the coordinates of the triangle's vertices as (4, 1), (6, 3), and (3, 8), we can substitute these values into the formula to find the centroid.

[ x_{\text{centroid}} = \frac{4 + 6 + 3}{3} = \frac{13}{3} ] [ y_{\text{centroid}} = \frac{1 + 3 + 8}{3} = \frac{12}{3} = 4 ]

So, the coordinates of the centroid are ((\frac{13}{3}, 4)).

To find the distance between the centroid and the origin, we can use the distance formula, which is the Pythagorean theorem in two dimensions:

[ d = \sqrt{(x_{\text{centroid}} - 0)^2 + (y_{\text{centroid}} - 0)^2} ]

Substitute the coordinates of the centroid into the formula:

[ d = \sqrt{(\frac{13}{3})^2 + 4^2} ] [ d = \sqrt{\frac{169}{9} + 16} ] [ d = \sqrt{\frac{169}{9} + \frac{144}{9}} ] [ d = \sqrt{\frac{313}{9}} ] [ d = \frac{\sqrt{313}}{3} ]

So, the distance between the centroid of the triangle and the origin is (\frac{\sqrt{313}}{3}).

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 ,1 )#. How far is the triangle's centroid from the origin?
- A line passes through #(3 ,6 )# and #(6 ,5 )#. A second line passes through #(4 ,3 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- A line passes through #(5 ,1 )# and #(6 ,5 )#. A second line passes through #(4 ,3 )#. 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 ,5 )# and a radius of #1 #. Circle B has a center at #(-1 ,1 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?
- A triangle has corners at #(5 ,6 )#, #(3 ,7 )#, and #(8 ,9 )#. How far is the triangle's centroid from the origin?

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