Question

The centroid of a rectangle of height h and width w is located at

• A. (h/2, w/2)
• B. (h/4, w/4)
• C. (w/3, h/3)
• D. (w, h)

Hint:

Centroid of Basic Shapes. The centroid of a rectangle is at the intersection of its diagonals, which is at the geometric center: halfway along its width and halfway along its height. If width=w, height=h, centroid is at (w/2, h/2) relative to a corner origin.

Answer 1

The Correct Option is A

The centroid of a geometric figure is its geometric center or the average position of all the points in the figure.
For simple symmetric shapes, the centroid lies at the center of symmetry.
A rectangle with width \(w\) and height \(h\) has two axes of symmetry passing through its center.
Let's assume the rectangle is placed with one corner at the origin (0,0), extending to \(w\) along the x-axis and \(h\) along the y-axis.
The center of symmetry along the width (x-direction) is at \(w/2\).
The center of symmetry along the height (y-direction) is at \(h/2\).
Therefore, the coordinates of the centroid are \((\frac{w}{2}, \frac{h}{2})\).
Option (1) gives (h/2, w/2).
This likely assumes coordinates are given as (y, x) or that h is along x and w along y.
In the standard (x,y) convention with width w along x and height h along y, the centroid is at (w/2, h/2).
Assuming option (1) meant (w/2, h/2) based on the values present, it is the correct location.