The question actually asks
for a definition of a DME Line of Position and there isn't
one........not a definitive one that we can find at least.
The CASA document states DME range.
Another sources states: "The line of position
produced by a distance measurement such as those produced by a DME
(distance-measuring equipment)." This is stating DME range.
DME Range = Slant Range.
Therefore, on this basis, I believe that the true correct answer is 'Slant Range', HOWEVER, it now appears that the examiner may have
opted for 'Ground Range'. We will not know the absolute answer to this question
until it turns up in an exam and someone scores 100%, whereby that person can
then confirm what answer they gave to that specific question.
BTW, Basic Area Nav equipment such as the Bendix King
KNS80 does not display calculated ground distance - it displays slant range
distance. When you are overhead the Beacon at a HEIGHT of 12000' it displays 2
NM (or thereabouts).