Find the center of mass of the rectangle `(1,-3)(4,-3)(4,5)(1,5)`

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The center of mass of the rectangle with vertexes (1, -3), (4, -3), (4, 5) and (1, 5) has to be determined. Assuming the material that the rectangle is made of has a uniform density, the center of mass of the rectangle lies at the intersection of its diagonals.

This is the intersection of the liens between (1, -3) and (4, 5) and between (4, -3) and (1, 5)

The line between (1, -3) and (4, 5) is (y +3)/(x - 1) = (8/3)

=> 3y + 9 = 8x - 8

=> y = (8x -17)/3

The line between (4, -3) and (1, 5) is (y +3)/(x - 4) = (8/-3)

=> -3y - 9 = 8x - 32

=> y = (8x - 23)/(-3)

(8x -17)/3 = (8x - 23)/(-3)

=> 8x - 17 = 23 - 8x

=> 16x = 40

=> x = 2.5

y = 1

**The center of mass is (2.5, 1)**

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