I figured I'll first implement a line drawing functionality, then have whatever "gems" it intersects be destroyed.
I'm sure there are better ways to implement this, but at such short notice, and without any prior experience with Construct, this is what I have for now:
Essentially, the line is just a series of short line segments each created with a scaled sprite. The original sprite is 1px by 4px. With 4px being the thickness of the line. Each segment is rotated and has its width set based on the touch position.