Answer:

Half past 9 in the morning is written as 9:30 a.m.
Here's an explanation of why the correct answer is option 'B':

Time in the morning
When we refer to time in the morning, we use the abbreviation "a.m." which stands for "ante meridiem" and means "before noon". It indicates that the time is in the morning hours.

Half past 9
When we say "half past 9", it means that 30 minutes have passed since 9 o'clock.

Reading the time
To read the time, we use the 12-hour clock system. The hours are represented by numbers from 1 to 12, and the minutes are represented by numbers from 0 to 59.

Minutes in the clock
The minutes in the clock can be divided into four quarters:
- From 0 to 14 minutes, it is considered the first quarter.
- From 15 to 29 minutes, it is considered the second quarter.
- From 30 to 44 minutes, it is considered the third quarter.
- From 45 to 59 minutes, it is considered the fourth quarter.

Half past the hour
When the time is half past the hour, it means that the minute hand points at 6 on the clock face. In the case of half past 9, the hour hand points at 9 and the minute hand points at 6.

Writing the time
To write the time, we use a colon (:) between the hours and minutes. In this case, since it is in the morning, we write "9:30 a.m."

Therefore, the correct answer to "How is half past 9 in the morning written?" is option 'B' - 9:30 a.m.