# A triangle has corners at #(5 ,2 )#, #(9 ,7 )#, and #(6 ,5 )#. How far is the triangle's centroid from the origin?

Distance of Centroid G from origin O is

To find the distance

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

To find the centroid of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid are given by the average of the x-coordinates and the average of the y-coordinates:

Centroid's x-coordinate (Cx) = (x1 + x2 + x3) / 3 Centroid's y-coordinate (Cy) = (y1 + y2 + y3) / 3

Using the given coordinates:

x1 = 5, y1 = 2 x2 = 9, y2 = 7 x3 = 6, y3 = 5

Cx = (5 + 9 + 6) / 3 = 20 / 3 ≈ 6.67 Cy = (2 + 7 + 5) / 3 = 14 / 3 ≈ 4.67

Now, to find the distance from the centroid to the origin (0, 0), you can use the distance formula:

Distance = √((Cx - 0)^2 + (Cy - 0)^2)

Plugging in the values:

Distance = √((6.67 - 0)^2 + (4.67 - 0)^2) Distance ≈ √(44.4889 + 21.8089) Distance ≈ √66.2978 Distance ≈ 8.14 (approximately)

So, the distance from the triangle's centroid to the origin is approximately 8.14 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.

- A line passes through #(9 ,2 )# and #( 3, 5 )#. A second line passes through #( 4, 8 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- Find the coordinates of all points whose distance from #(0,-3)# is #\sqrt{5}# and whose distance from #(3,-4)# is #\sqrt{5}#?
- A line passes through #(2 ,2 )# and #(1 ,2 )#. A second line passes through #( 7, 4 )#. 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 #(2 ,-1 )# and a radius of #3 #. Circle B has a center at #(-3 ,6 )# and a radius of #1 #. Do the circles overlap? If not, what is the smallest distance between them?
- What are the parametric equations for the line of intersection of the planes #x + y + z = 7# and #x + 5y + 5z = 7#?

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