Final answer:
In a line segment XY with midpoint A, XA is equal to AY, XA is half the length of XY, and XY is the sum of XA and AY. Statement D is incorrect because AY is not equal to XY.
Step-by-step explanation:
The student is asking about the properties of line segments and their midpoints. In the context of a line segment XY with the midpoint A, the correct statement is: XA is equal to AY. This is because the midpoint of a line segment divides the segment into two equal parts. It is also true that XY is the sum of XA and AY, as these two segments together make up the entire length of XY. Therefore, both statements A and C are correct. Statement B, stating that 'XA is half the length of XY,' is also correct because XA is indeed half of the full segment XY. However, statement D is incorrect because AY is not equal to the whole length of XY, but rather, it is equal to the length of XA, as they are both halves of XY.