# ...centroid

• Nov 19th 2006, 07:05 PM
eureka
...centroid
Pls help the following question;

The centroid (centre) of an object is the average of its x and y coordinates. A pentagonal object has vertices as follows;

Vertex A B C D E
Coordinates (1,2) (4,2) (5,5) (4,6) (2,5)

a) Calculate the centroid of the pentagon
b) Find M, the 3x3 matrix that scales the pentagon by a scale factor of 2.5 about ist centroid

Thank you very much.
• Nov 19th 2006, 07:13 PM
ThePerfectHacker
Quote:

Originally Posted by eureka
Pls help the following question;

The centroid (centre) of an object is the average of its x and y coordinates. A pentagonal object has vertices as follows;

I never knew that, it seems to be the case for polygonal objects, right? (It is certainly simpler than what I would have used).

Quote:

a) Calculate the centroid of the pentagon
Using what you said,
The average of the x's is:
$\displaystyle x=\frac{1+4+5+4+2}{5}=3.2$

$\displaystyle y=\frac{2+2+5+6+5}{5}=4$
• Nov 19th 2006, 07:54 PM
eureka
Thanks for your help for question a, but how about question b?