Can a Generation 9 ipad output to a projector?

If you what you really have is the 9th Generation iPad you mention, then you will need a Lightning Digital AV adapter: click here ➡️ Lightning Digital AV Adapter - Lightning to HDMI - Apple

This will let you connect an HDMI cable from the iPad to the Projector and the iPad will mirror its screen to it.

Unless you need the slightly newer, and slightly faster, CPU, slightly better camera and the ability to record 4K videos, I would say the 9th gen is fine just for presenting through a projector.

You can compare them here: link ➡️ Compare iPads - 9th Generation,10thGeneration,iPad Air 5th Generation - Apple.com

Most models of iPad support both HDMI and/or VGA with an the appropriate adapter. The fifth and sixth generation iPad Pro also support DP Alt Mode over USB-C - but this is perhaps irrelevant unless the projector supports DisplayPort.

Assuming that you intend to use a sixth generation iPad Pro 12.9” (as implied by the tags appended to your post), perhaps the easiest option for HDMI would be the Apple USB-C Digital AV Multiport Adapter:

https://store.apple.com/uk/xc/product/MUF82ZM/A

You’ll obviously require a good quality HDMI cable - 4K being recommended as it will work well with both modern and older versions of HDMI.

You connect an external HDMI Display/Projector - and simultaneously connect your iPad Power Adapter to save reliance upon the iPad battery during the presentation. You also usefully have a USB3 Type-A connector for other USB accessories and/or USB storage devices.

As a [perhaps less useful] alternative, you might also consider the Apple USB-C VGA Multiport Adapter:

https://store.apple.com/uk/xc/product/MJ1L2ZM/A

The iPad9 and iPad10 have some differences which may swing your choice one way or other. You can directly compare all models of iPad and their specifications here:

https://www.apple.com/ipad/compare/?modelList=ipad-10th-gen,ipad-9th-gen,ipad-air-5th-gen

The iPad10 benefits from the much more useful and flexible USB-C connectivity - a more advanced CPU - and moves the front-facing camera to the top-centre of the iPad screen when viewed in Landscape orientation.