No ... I would say Perth is more centrally situated.
..................................................., really. Because, even though the city's frequently referred to as being "The Gateway To The Highlands", it's not an accurate description IMO, since - due to the shape of Scotland - its border with the north of England on the eastern side starts higher up than it does in the south west.
Consequently, in actual mileage terms, we're probably closer to the Border on the eastern side of the country.
... you will be.