Answer
The location of the center of mass is $(1.92~m, 1.38~m)$
Work Step by Step
We can find the x-coordinate of the center of mass:
$x_{com} = \frac{(4.0~kg)(4.0~m)+(6.0~kg)(2.0~m)+(3.0~kg)(-1.0~m)}{4.0~kg+6.0~kg+3.0~kg}$
$x_{com} = \frac{25.0~kg~m}{13.0~kg}$
$x_{com} = 1.92~m$
We can find the y-coordinate of the center of mass:
$y_{com} = \frac{(4.0~kg)(0~m)+(6.0~kg)(4.0~m)+(3.0~kg)(-2.0~m)}{4.0~kg+6.0~kg+3.0~kg}$
$y_{com} = \frac{18.0~kg~m}{13.0~kg}$
$y_{com} = 1.38~m$
The location of the center of mass is $(1.92~m, 1.38~m)$.
