The oldest word here is צֶלֶם, an image or likeness, the very word in b'tzelem Elohim, "in the image of God". Modern Hebrew took that ancient root and made it the whole vocabulary of photography: the verb to photograph, the photographer, the photo, the camera. So one root spans three thousand years, from a carved likeness to a digital snapshot. Watch the mould do the work: the same three letters become the agent, the act, the shot, and the machine. Every word here is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
The active verb sits in pi'el, לְצַלֵּם. Its passive partner pu'al (to be photographed) and the reflexive hitpa'el לְהִצְטַלֵּם (to have one's picture taken, where the ת becomes ט before צ) are fully in use even though no plain noun derived from them appears in this verified family.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.