住
zhù
Why 'to live somewhere' and 'to hold tight' share one character: 住
The picture Something in motion sticks to one spot and stops coming loose. 走 leaves the spot and moves off; 住 sticks to the spot and stops moving at all.
Where the picture shows up in 住
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stay stuck to one home
我住在公司附近。
wǒ zhù zài gōngsī fùjìn
I live near the office.
Every night the same door opens and you lay your body down in the same room.
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stay put for a while
您住几号房？
nín zhù jǐ hào fáng
Which room are you staying in?
Your suitcase stands in the corner of a hotel room while you stay stuck to that room for a few days.
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stuck in your hand
快抓住他！
kuài zhuā zhù tā
Quick, grab hold of him!
The hand that shot out has his collar in its fist and won't let go.
The 住 in 抓住 adds the result: you grabbed it and it didn't slip away.
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won't stick in your head
这个词我记不住。
zhège cí wǒ jì bu zhù
I just can't remember this word.
The word you memorized slides off the surface of your mind and drops away again.
记不住 is memorizing that refuses to stick.
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words stuck in your throat
他的话把我问住了。
tā de huà bǎ wǒ wèn zhù le
What he said left me speechless.
The reply that was on its way out sets hard in your throat and your mouth won't open.
All of it in one picture
住 is something in motion sticking to one spot and refusing to come loose. Stick to one house and you live there; stick to a room for a few days and you're staying there. If what you grabbed can't come loose, that's 抓住; if the word won't stick to your mind, that's 记不住. Even words setting hard in your throat is the same picture — so 住 always adds the result that something stuck and did not come off.