一点半 means 1:30. 我等了一点半 doesn't make sense, because nobody will say "I wait for 1:30". It should be "I will wait for you until 1:30."

If you want to express how long you wait for someone, it would be "一个半小时", which means half and an hour. E.g. 我已经等了你一个半小时。I have already waited for you for half and an hour.

一点半 is a time point, not an interval. Like in English, we say 'I have waited for one and half hour', not 'I waited for 1:30'. You can change the character '了' to '到'.

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