Question

If the Earth and distant stars were stationary (motionless) in space, what would we observe about the wavelength from these stars?
A.Wavelengths measured would match the actual wavelengths emitted.
B.Wavelengths measured would be shorter than the actual wavelengths emitted.
C.Wavelengths measured would be longer than the actual wavelengths emitted.

If a star is moving toward us in space, what would we observe about the wavelength from these stars?

A.Wavelengths measured would be shorter than the actual wavelengths emitted.

B.Wavelengths measured would match the actual wavelengths emitted.

C.Wavelengths measured would be longer than the actual wavelengths emitted.

Answer 1

There's no such thing as "stationary in space".  But if the distance
between the Earth and some stars is not changing, then (A) wavelengths
measured here would match the actual wavelengths emitted from these
stars. 

If a star is moving toward us in space, then (A) Wavelengths measured
would be shorter than the actual wavelengths emitted from that star.

In order to decide what's actually happening, and how that star is moving, 
the trick is:  How do we know the actual wavelengths the star emitted ?