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

Answer 1

Distance of Centroid G from origin O is #color(green)(GO = 8.1377)#

#G_x = (5 + 9 + 6) / 3 = 20/3#

#G_y = (2 + 7 + 5) / 3 = 14/3#

To find the distance #G(20/3, 14/3)# to #O (0, 0)# where G is the centroid and O the origin.

#GO = d = sqrt(((20/3) -0)^2 + ((14/3)-0)^2) = 8.1377#

Sign up to view the whole answer

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

Sign up with email
Answer 2

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.

Sign up to view the whole answer

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

Sign up with email
Answer from HIX Tutor

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.

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7