I think something might have changed since this thread was last updated - the cost of active HDMI to Display Port cables has dropped.
I ordered one from Amazon for £24.99 to connect to a 2nd hand HP monitor that I picked up for £5. The one I ordered came with a female DP port and so also required a male - male DP cable to connect it to the monitor.
Because it is an active cable it means your Raspberry Pi (3 B in this case) + cable require two USB ports to provide power, which fortunately wasn't a problem for me because the Pi is powered by a 6 port Anker USB power supply that has free ports.
However this arrangement is not 100% trouble free. There is a niggling annoyance AFTER
shutting down the Pi. Once the Pi has been shutdown and the USB power cable has been unplugged from the Pi, the Pi remains powered on (red LED remains illuminated). When the Pi is in this pseudo-shutdown state, it does not reboot if the power cable is reattached to it. It is only once the DP adaptor is also unplugged from the Pi, or the DP adaptor's power cable is unplugged from the PSU that the Pi finally shuts down completely. After re-reading all the comments about the cable on Amazon I noticed that one other person has commented on this behaviour.
Interestingly once the Pi has booted the power cable for the HDMI-DP adaptor can be unplugged from the PSU and the monitor continues to work.
It may be that other HDMI-DP cables do not exhibit this peculiar behaviour. The one I bought can be found at: https://smile.amazon.co.uk/dp/B07G796JF8