Why does a spherometer have three legs​

Recall from geometry that three points determine a plane, so the three legs will always touch the glass.One complete turn of the central screw of the spherometer raises or lowers the center point a set distance which is determined by the size of the thread of the screw and the radius of the disc.

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)