Step 1 :Let the wall length be \(l = 18\) ft and the wall height be \(h = 10\) ft.
Step 2 :Find the horizontal midpoint: \(\frac{l}{2} = \frac{18}{2} = 9\) ft.
Step 3 :Find the vertical midpoint: \(\frac{h}{2} = \frac{10}{2} = 5\) ft.
Step 4 :\(\boxed{\text{Final Answer: To hang the art at the midpoint of the wall, Peter should place the wall anchor 9 feet from the side wall and 5 feet from the ceiling.}}\)