1. ## Centroid

Hi everyone,

I have a problem i can't figure out...

I want to calculate the centroid of a tilted rectangle in a coordinate system (See image) based on the following informations

I know the Y coordinate of corner A
I know the slope of the line b to the X axis based on two known points
I know lenght of a and b

From a given point on line b I need to find the centroid?

So given an example what would the centroid be

a = 10
b = 15

Y coordinate of A is 5

The slope of line b to X can be calculated from two given points 0,10 and 10,15

From coordinate 0,10 how to
calculate the centroid?

All the best,

Kris

2. ## Re: Centroid

line AD has equation $y = \dfrac{x}{2}+10 \implies \text{ point A } = (-10,5)$

let $\theta$ be the angle between line AD and the horizontal, and $\phi$ be the angle between line AD and diagonal AC. Label the centroid (intersection of the two diagonals) point E. (reference attached diagram)

$|AE| = \sqrt{5^2 + 7.5^2} = \dfrac{5\sqrt{7}}{2}$

$\tan{\theta} = \dfrac{1}{2}$, $\tan{\phi} = \dfrac{2}{3}$

$\tan(\theta+\phi) = \dfrac{7}{4}$

centroid x-value, $\bar{x} = -10 + \dfrac{5\sqrt{7}}{2}\cos(\theta+\phi) = -10 + \dfrac{5\sqrt{7}}{2} \cdot \dfrac{4}{\sqrt{65}}$

centroid y-value, $\bar{y} = 5 + \dfrac{5\sqrt{7}}{2}\sin(\theta+\phi) = 5 + \dfrac{5\sqrt{7}}{2} \cdot \dfrac{7}{\sqrt{65}}$

3. ## Re: Centroid

Thanks i completely see it now!!