# 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...

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tonys538 | Student

An easier way to determine the center of mass of the rectangle with vertices (1, -3), (4, -3), (4, 5) and (1, 5) is to look at the coordinates of the points.

The center of mass is the point equidistant from the 4 points.

The points (1, -3) and (4, -3) have a common y-coordinate, -3. The points (4, 5) and (1, 5) have a common y-coordinate 5. The y-coordinate of the point equidistant from the points is equal to (-3 + 5)/2 = 2/2 = 1

Similarly, the points (4, -3) and (4, 5) have a common x-coordinate 4 and the points (1, -3) and (1, 5) have a common x-coordinate 1. The x-coordinate of the equidistant point is (1 + 4)/2 = 2.5

This gives the coordinates of the center of mass as (2.5, 1)