A very good laser has a beam divergence of tenths of milliradians, or 0.01 degrees. At the radius of planet 9, this is a very large beam, and we'd have a hard time putting out enough power to compete with the sun.
Furthermore, the sky has an area of 40,000 square degrees. Our little laser beam projects a circle with an area of 0.0000785 square degrees. You'd need to aim at 500 million spots to see the whole sky.
That's smaller than I expected. To convert that into human scale sqrt(500 million) = 22360, in millimeters that's around 22 meters (72 ft).
So if we had a square wall 22 meters by 22 meters we could paint a grid of 1 mm by 1 mm squares on it and end up with around 500 million squares.
Then we'd need to stand there in front of the wall with a laser pointer and shine the laser at each individual square and check the light bouncing back at us.
And there's uncertainty in whether your measurement is accurate.
And there's a background of other illuminated squares that can interfere with your readings.
And you're spinning while this is going on.
And the target square is continually moving. You might have just missed it.
1. Build a Dyson sphere around the sun.
2. Capture all the mass in the solar system to build a giant freaking laser.
3. Use the energy to from the Dyson sphere to power the laser.
4. Melt your entire civilization.
The scale isn't lost on me. I'm aware of how much ground would need to be covered when you get out that far, and I figured that might be a pretty damning factor. That said, you wouldn't need to sweep it across the entire surface, only enough of the surface to rule out any interfering debris between us and the object. Wouldn't take much. We would need VERY accurate models of the orbit based on effects on other bodies, but it's hard to totally rule it out in my head.
Edit - podcast link https://www.preposterousuniverse.com/podcast/2018/08/27/epis...
:)
In all seriousness, that would definitely kill any possibility. Sweeping an entire orbit at the resolution needed to hit something smaller than Uranus/Neptune would take eons.
I think someone should re-imagine all of Star Wars as hard Sci-fi set in the vicinity of a system like Alpha Centauri. That's still a vast setting.
Douglas Adams, The Hitchhiker's Guide to the Galaxy
That's before you get to the problem that space is ridiculously big, and sweeping it across the entirety of the surface of the imaginary sphere that might contain planet #9 would probably take millions of years (citation needed).