"you have a flat piece of plastic of uniform density ρ in the shape of a right triangle. the legs of the triangle are given as a and b. where is the center of mass of this triangle? using the coordinate system given, enter the coordinates of the center of mass in terms of a and b."

Since the piece of plastic with uniform density is a Right angled triangle ;

For a right angled triangle the centroid and the center of mass is the same. the center of mass can be determined by taking the average value of the three legs of the right angled triangle.

Therefore to actually determine the  location of the center of mass in the triangle, look for  the point of intersection between 1/3 height and 1/3 base length of the triangle.

Hence we can conclude that The center of mass of the triangle is located at the point where ; 1/3 base length and 1/3 height of the triangle intersects and The coordinates of the center of mass  is ; ( a/3 , b/3 ).

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