鏡 and 時計: checking reflections and time
Distinguish what is checked from the condition of the object when looking at a mirror or clock.
Checking with a mirror
鏡, read かがみ, means mirror. 鏡で髪形を確認しました。 means checking one's hairstyle in a mirror.
鏡に顔が映っています。 says that a face is reflected in a mirror. The face is the reflected object, not the surface reflecting the mirror.
Checking with a clock
時計, read とけい, means clock or watch. 時計を見て、時間を確かめました。 means looking at a clock or watch to check the time.
時計が五分遅れています。 says that the clock is five minutes slow. It does not say that a person is five minutes late for an appointment.
Objects and responses
鏡を壁に掛けました。 means hanging a mirror on a wall. This is placing the object, not observing it as in 鏡を見る.
時計を見ましたが、時刻は覚えていません。 says that someone looked at the clock but does not remember the time. Separate looking from remembering.
Does 時計が五分遅れています describe a person arriving late?
Show the answer and why
No. It describes a clock showing a time five minutes behind the actual time.

