# A triangle has corners at #(9 ,3 )#, #(7 ,5 )#, and #(3 ,1 )#. How far is the triangle's centroid from the origin?

The answer is

Therefore,

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

The centroid of a triangle is located at the average of its three vertices.

Let's denote the coordinates of the vertices as follows:

( A(9, 3) ),

( B(7, 5) ),

( C(3, 1) ).

The centroid ( G ) is given by the formula:

( G\left(\frac{{x_A + x_B + x_C}}{3}, \frac{{y_A + y_B + y_C}}{3}\right) ).

Substituting the coordinates, we get:

( G\left(\frac{{9 + 7 + 3}}{3}, \frac{{3 + 5 + 1}}{3}\right) = G\left(\frac{19}{3}, \frac{9}{3}\right) ).

So, the coordinates of the centroid ( G ) are ( \left(\frac{19}{3}, 3\right) ).

Using the distance formula, the distance between ( G ) and the origin is:

( \sqrt{\left(\frac{19}{3}\right)^2 + 3^2} = \sqrt{\frac{361}{9} + 9} = \sqrt{\frac{361 + 81}{9}} = \sqrt{\frac{442}{9}} ).

Hence, the distance between the centroid and the origin is ( \frac{\sqrt{442}}{3} ) units.

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.

- What is the perimeter of a triangle with corners at #(6 ,4 )#, #(9 ,2 )#, and #(5 ,7 )#?
- What is an equation of the line that goes through point (8, −9) and whose slope is undefined?
- Circle A has a center at #(-6 ,4 )# and a radius of #9 #. Circle B has a center at #(1 ,-5 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?
- Circle A has a center at #(5 ,4 )# and a radius of #3 #. Circle B has a center at #(6 ,-8 )# and a radius of #2 #. Do the circles overlap? If not, what is the smallest distance between them?
- Circle A has a center at #(4 ,-8 )# and a radius of #3 #. Circle B has a center at #(-2 ,-2 )# and a radius of #2 #. 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