Calculating Centroids of a Triangle: Why Do Formulas Switch?

[CivilSigma]

Homework Statement

Hello. In class we learned how to calculate centroids of a triangle. For the y-coordinate we use the formula height/3 and for the x we use 2/3 * base

Homework Equations

In the diagram, If I want to calculate the y coordinate , I do 72 (which is the proposed height)/ 3 ; only to get y=24 which is incorrect.

It turns out that to find the y-coordinate in this case we must do 2/3*height. Why is that so? This is really confusing.
Why did the formulas to calculating 'y' and 'x' values switch?

Thank you for your time.

 

[Mark44]

Homework Statement

Hello. In class we learned how to calculate centroids of a triangle. For the y-coordinate we use the formula height/3 and for the x we use 2/3 * base

Homework Equations

In the diagram, If I want to calculate the y coordinate , I do 72 (which is the proposed height)/ 3 ; only to get y=24 which is incorrect.

It turns out that to find the y-coordinate in this case we must do 2/3*height. Why is that so?

Because the triangle is upside down. The "base" is at the top and you have to measure 1/3 of the way down.

This is really confusing.
Why did the formulas to calculating 'y' and 'x' values switch?

Thank you for your time.

 

[CivilSigma]

But the height is still 72? and one more thing, when we say the height do we automatically pick the longest side of the triangle?

Edit: Okay I see what you mean now. If I do h/3 , I get 24 but that is from the top not the bottom of the plane.

However, how would you calculate the x-coordinate?

 

[Mark44]

But the height is still 72? and one more thing, when we say the height do we automatically pick the longest side of the triangle?

Usually, what we call the base is at the bottom and horizontal, and the altitude or height is the vertical distance from the base to the opposite vertex. This triangle is oriented so that the base is at the top. When you calculate the area using A = (1/2) b * h, any side can be considered the base.

Edit: Okay I see what you mean now. If I do h/3 , I get 24 but that is from the top not the bottom of the plane.

However, how would you calculate the x-coordinate?

You have the formula in your first post.

 

[rezeew]

Hello,

Calculating the centroid of a triangle involves finding the point of intersection of the three medians of the triangle. The median is the line segment that connects a vertex of the triangle to the midpoint of the opposite side.

In order to find the y-coordinate of the centroid, we need to find the average of the y-coordinates of the three vertices. This can be done by dividing the sum of the y-coordinates by 3. However, in the formula you mentioned, the height is being used instead of the y-coordinate of the vertex. This is because in a right triangle, the height is equal to the y-coordinate of the vertex.

As for the x-coordinate, we need to find the average of the x-coordinates of the three vertices. This can be done by dividing the sum of the x-coordinates by 3. However, in the formula you mentioned, the base is being used instead of the x-coordinate of the midpoint of the base. This is because the base of a right triangle is equal to twice the x-coordinate of the midpoint of the base.

So, the formulas for calculating the y-coordinate and x-coordinate of the centroid of a triangle are based on the properties of right triangles. I hope this clears up the confusion.

Thank you.