Answer
The center of gravity is at the point $0.988~m$ from the left side of the door and at a height of $1.50~m$ from the bottom of the door.
Work Step by Step
In general the center of gravity is: $x_{cog} = \frac{\sum (w_i~x_i)}{\sum w_i}$, where $w_i$ is the weight of each object, and $x_i$ is the position of each object.
Let the bottom left corner of the door be the origin. We can find the x-coordinate of the center of gravity:
$x_{cog} = \frac{(5.0~N)(0.25~m)+(300.0~N)(1.00~m)}{5.0~N+300.0~N}$
$x_{cog} = 0.988~m$
By symmetry, the y-coordinate of the center of gravity is $y_{cog} = 1.50~m$
The center of gravity is at the point $0.988~m$ from the left side of the door and at a height of $1.50~m$ from the bottom of the door.
