Not a quiz question, but if you need students to be able to draw freehand it can be done using a Poodll Assignment Submission set up as a submission type of, Whiteboard. Just be aware that Poodll Assignment Submission requires the Poodll Filter and does cost money.
Works really well if you have some kind of tablet with a pen. Also works reasonably well with a mouse if you practice.
Maybe you can use the essay question type (https://docs.moodle.org/310/en/Essay_question_type) and in the description you ask the student to copy/paste the image and draw on it on the application on the tablet and after save it upload it in the question answer. In fact, it's a little bit more tricky. But it's a thing that everyone should be able to do now or almost : )
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(I have installed this plugin : https://moodle.org/plugins/qtype_drawing and it do what you want, I think. You can have a background image and draw on it) The plugin doesn't work on Moodle 4.0 for now.
Thanks, we already considered the Essay option, but it's a bit too convoluted.
We also considered the ETH qtype, and it's very limited ...
Thank you very much for your support.
I use drawing in one course I have. I think drawing is one way to get students to remember what they are learning online. And remembering is key because a lot of people don't remember what they are studying online.
I use it in assignments and have them submit their drawing in an assignment. I try to teach students activities that they can use and they often learn activities by watching them done on video but to check their retention I have them draw some out. Students have said they thought it did help. And it's a little less boring than just repeating the steps with text.
They just draw on paper take a picture of it and submit it.