# A triangle has corners at #(4 ,1 )#, #(8 ,3 )#, and #(3 ,5 )#. How far is the triangle's centroid from the origin?

Triangle’s centroid is 5.83 away from origin.

Centroid

Coordinates of centroid G is

Distance from origin

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

The centroid of a triangle is the point where the three medians intersect. To find the centroid, we calculate the average of the coordinates of the three vertices. Then, we find the distance between the centroid and the origin using the distance formula.

Given the vertices of the triangle are (4, 1), (8, 3), and (3, 5), the centroid can be found by averaging the x-coordinates and the y-coordinates separately.

The x-coordinate of the centroid, ( \bar{x} ), is the average of the x-coordinates of the vertices: [ \bar{x} = \frac{4 + 8 + 3}{3} = \frac{15}{3} = 5 ]

The y-coordinate of the centroid, ( \bar{y} ), is the average of the y-coordinates of the vertices: [ \bar{y} = \frac{1 + 3 + 5}{3} = \frac{9}{3} = 3 ]

So, the centroid of the triangle is at (5, 3).

Now, we calculate the distance between the centroid (5, 3) and the origin (0, 0) using the distance formula: [ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ] [ d = \sqrt{(5 - 0)^2 + (3 - 0)^2} ] [ d = \sqrt{5^2 + 3^2} ] [ d = \sqrt{25 + 9} ] [ d = \sqrt{34} ]

So, the distance between the centroid of the triangle and the origin is ( \sqrt{34} ).

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.

- Circle A has a center at #(1 ,8 )# and an area of #15 pi#. Circle B has a center at #(5 ,3 )# and an area of #24 pi#. Do the circles overlap?
- A triangle has corners at #(9 ,5 )#, #(2 ,7 )#, and #(3 ,2 )#. How far is the triangle's centroid from the origin?
- How many values of x between 0.01 and 1 does the graph #sin(1/x)# cross the x-axis?
- A triangle has corners at #(9 ,1 )#, #(2 ,4 )#, and #(5 ,8 )#. How far is the triangle's centroid from the origin?
- Circle A has a center at #(12 ,2 )# and an area of #13 pi#. Circle B has a center at #(3 ,6 )# and an area of #28 pi#. Do the circles overlap?

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