Display apparatus and control method for display apparatus

A display apparatus that displays an image on a display surface, the display apparatus comprising:

• a determining unit configured to determine whether a distance between an indicator for indicating a position on the display surface and a distance measuring unit configured to measure a distance to the indicator is a first threshold or less;
• a switching unit configured to switch, when a mode of the display apparatus is a first mode, the mode from the first mode to a second mode when it is determined that the distance between the indicator and the distance measuring unit is the first threshold or less;
• a detecting unit configured to detect the position on the display surface indicated by the indicator;
• and
• a processing unit configured to, when indication of a first position on the display surface is detected, perform first processing corresponding to the first position when the mode is the first mode and perform second processing different from the first processing corresponding to the first position when the mode is the second mode.