Answer
The x coordinate of the center of mass of the remaining piece is $~~-\frac{d}{4}$
Work Step by Step
The area of the original square plate was $36d^2$
The area of the square plate that was removed is $4d^2$
The area of the remaining piece is $32d^2$
Therefore, if the mass of the square piece that was removed is $M$, then the mass of the remaining piece is $8M$
Before the square piece was removed, the x coordinate of the center of mass was 0.
By symmetry, the x coordinate of the center of mass of the square piece that was removed is $2d$
Let $x$ be the center of mass of the remaining piece. We can find $x$:
$\frac{(8M)(x)+(M)(2d)}{9M} = 0$
$(8M)(x)+(M)(2d)= 0$
$(8M)(x)= -(M)(2d)$
$8x= -2d$
$x = -\frac{d}{4}$
The x coordinate of the center of mass of the remaining piece is $~~-\frac{d}{4}$
