A thin, uniform lamina is cut into the shape of an equilateral triangle of side length 0.60m. The triangle is suspended from one of its vertices by a light string so that it can swing freely in a vertical plane. A Cartesian coordinate system is chosen with its origin at that vertex, the positive x–axis along one edge, and the positive y–axis along another edge.
a. Part 1: a) List all symmetry lines of the lamina and state how they constrain the coordinates of its center of mass after the triangle comes to rest.
b. Part 2: b) Use symmetry arguments to determine the x– and y–coordinates of the center of mass relative to the chosen origin without performing any integration.
c. Part 3: c) Derive an expression for, and then calculate, the perpendicular distance from any side of the triangle to the center of mass. Give a numerical answer in meters.