centroid of the L-shaped segment shown in the figure below is at coordinates ( $( \bar { x } , \bar { y } ) \text { (in.): }$

Question

Quizplus · Accepted Answer

To find the centroid of a L-shaped segment, we can divide it into two rectangles and then take the weighted average of their centroids.

First rectangle: 
Width = 2 in 
Length = 3 in 
Area = 2 in * 3 in = 6 in^2 
Centroid coordinates: 
x = 1 in + 2 in/2 = 2 in 
y = 0 + 3 in/2 = 1.5 in

Second rectangle: 
Width = 1 in 
Length = 2 in 
Area = 1 in * 2 in = 2 in^2 
Centroid coordinates: 
x = 1 in/2 = 0.5 in 
y = 1.5 in + 2 in/2 = 2.5 in

Now we take the weighted average of the two centroids: 
x-bar = (6 in^2 * 2 in + 2 in^2 * 0.5 in) / (6 in^2 + 2 in^2) = 2 in 
y-bar = (6 in^2 * 1.5 in + 2 in^2 * 2.5 in) / (6 in^2 + 2 in^2) = 1.5 in

Therefore, the centroid of the L-shaped segment is at coordinates (2.0, 1.5)

Centroid of the L-Shaped Segment Shown in the Figure Below (xˉ,yˉ) (in.): ( \bar { x } , \bar { y } ) \text { (in.): }(xˉ,yˉ​) (in.):

Centroid of the L-Shaped Segment Shown in the Figure Below $( \bar { x } , \bar { y } ) \text { (in.): }$