expression, i-adjective
unthinkable; preposterous; out of the question
Expresses that something is so absurd or impossible that it cannot even be considered. Often used in negative contexts to reject an idea outright.
彼がそんなことをするなんて図がない。
It's unthinkable that he would do such a thing.
この値段で買えるなんて図がない話だ。
It's preposterous to think you can buy it at this price.
ありえない is a more common and direct way to say 'impossible' or 'unbelievable', while 図がない is a set phrase emphasizing that something is beyond consideration or absurd.
とんでもない is used to strongly deny or reject something as outrageous, similar in strength but more versatile; 図がない is more specifically about something being unthinkable or not even worth entertaining.
The phrase combines 図 (zu, 'plan' or 'intention') with がない (ga nai, 'there is no'), literally meaning 'there is no plan (for such a thing)'. The exact historical derivation is uncertain, but it has been used idiomatically to mean 'unthinkable' or 'out of the question'.